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Ein Faktor ist ",[568,724,726,751],{"className":725},[571],[568,727,729],{"className":728},[575],[577,730,731],{"xmlns":579},[581,732,733,748],{},[584,734,735,739,741,743,745],{},[598,736,738],{"stretchy":737},"false","(",[590,740,592],{},[598,742,600],{},[590,744,605],{},[598,746,747],{"stretchy":737},")",[609,749,750],{"encoding":611},"(a + b)",[568,752,754,777],{"className":753,"ariaHidden":617},[616],[568,755,757,761,765,768,771,774],{"className":756},[621],[568,758],{"className":759,"style":760},[625],"height:1em;vertical-align:-0.25em;",[568,762,738],{"className":763},[764],"mopen",[568,766,592],{"className":767},[630,634],[568,769],{"className":770,"style":674},[673],[568,772,600],{"className":773},[678],[568,775],{"className":776,"style":674},[673],[568,778,780,783,786],{"className":779},[621],[568,781],{"className":782,"style":760},[625],[568,784,605],{"className":785},[630,634],[568,787,747],{"className":788},[789],"mclose",", der andere ein quadratischer Term.",[564,792,793,794,1244,1245,1322,1323,1457,1458,1514],{},"Der zweite Faktor ",[568,795,797,870],{"className":796},[571],[568,798,800],{"className":799},[575],[577,801,802],{"xmlns":579},[581,803,804,867],{},[584,805,806,812,815,817,819,821,827,830,851,853,861],{},[587,807,808,810],{},[590,809,592],{},[594,811,596],{},[598,813,814],{},"−",[590,816,592],{},[590,818,605],{},[598,820,600],{},[587,822,823,825],{},[590,824,605],{},[594,826,596],{},[598,828,829],{},"=",[587,831,832,849],{},[584,833,834,836,838,840,847],{},[598,835,738],{"fence":617},[590,837,592],{},[598,839,814],{},[841,842,843,845],"mfrac",{},[590,844,605],{},[594,846,596],{},[598,848,747],{"fence":617},[594,850,596],{},[598,852,600],{},[841,854,855,858],{},[594,856,857],{},"3",[594,859,860],{},"4",[587,862,863,865],{},[590,864,605],{},[594,866,596],{},[609,868,869],{"encoding":611},"a^2 - ab + b^2 = \\left(a - \\frac{b}{2}\\right)^2 + \\frac{3}{4}b^2",[568,871,873,917,937,983,1139],{"className":872,"ariaHidden":617},[616],[568,874,876,879,908,911,914],{"className":875},[621],[568,877],{"className":878,"style":626},[625],[568,880,882,885],{"className":881},[630],[568,883,592],{"className":884},[630,634],[568,886,888],{"className":887},[638],[568,889,891],{"className":890},[642],[568,892,894],{"className":893},[646],[568,895,897],{"className":896,"style":651},[650],[568,898,899,902],{"style":654},[568,900],{"className":901,"style":659},[658],[568,903,905],{"className":904},[663,664,665,666],[568,906,596],{"className":907},[630,666],[568,909],{"className":910,"style":674},[673],[568,912,814],{"className":913},[678],[568,915],{"className":916,"style":674},[673],[568,918,920,924,928,931,934],{"className":919},[621],[568,921],{"className":922,"style":923},[625],"height:0.7778em;vertical-align:-0.0833em;",[568,925,927],{"className":926},[630,634],"ab",[568,929],{"className":930,"style":674},[673],[568,932,600],{"className":933},[678],[568,935],{"className":936,"style":674},[673],[568,938,940,943,972,976,980],{"className":939},[621],[568,941],{"className":942,"style":651},[625],[568,944,946,949],{"className":945},[630],[568,947,605],{"className":948},[630,634],[568,950,952],{"className":951},[638],[568,953,955],{"className":954},[642],[568,956,958],{"className":957},[646],[568,959,961],{"className":960,"style":651},[650],[568,962,963,966],{"style":654},[568,964],{"className":965,"style":659},[658],[568,967,969],{"className":968},[663,664,665,666],[568,970,596],{"className":971},[630,666],[568,973],{"className":974,"style":975},[673],"margin-right:0.2778em;",[568,977,829],{"className":978},[979],"mrel",[568,981],{"className":982,"style":975},[673],[568,984,986,990,1130,1133,1136],{"className":985},[621],[568,987],{"className":988,"style":989},[625],"height:1.4341em;vertical-align:-0.35em;",[568,991,994,1105],{"className":992},[993],"minner",[568,995,997,1007,1010,1013,1016,1019,1099],{"className":996},[993],[568,998,1002],{"className":999,"style":1001},[764,1000],"delimcenter","top:0em;",[568,1003,738],{"className":1004},[1005,1006],"delimsizing","size1",[568,1008,592],{"className":1009},[630,634],[568,1011],{"className":1012,"style":674},[673],[568,1014,814],{"className":1015},[678],[568,1017],{"className":1018,"style":674},[673],[568,1020,1022,1026,1096],{"className":1021},[630],[568,1023],{"className":1024},[764,1025],"nulldelimiter",[568,1027,1029],{"className":1028},[841],[568,1030,1033,1087],{"className":1031},[642,1032],"vlist-t2",[568,1034,1036,1082],{"className":1035},[646],[568,1037,1040,1056,1067],{"className":1038,"style":1039},[650],"height:0.8801em;",[568,1041,1043,1047],{"style":1042},"top:-2.655em;",[568,1044],{"className":1045,"style":1046},[658],"height:3em;",[568,1048,1050],{"className":1049},[663,664,665,666],[568,1051,1053],{"className":1052},[630,666],[568,1054,596],{"className":1055},[630,666],[568,1057,1059,1062],{"style":1058},"top:-3.23em;",[568,1060],{"className":1061,"style":1046},[658],[568,1063],{"className":1064,"style":1066},[1065],"frac-line","border-bottom-width:0.04em;",[568,1068,1070,1073],{"style":1069},"top:-3.394em;",[568,1071],{"className":1072,"style":1046},[658],[568,1074,1076],{"className":1075},[663,664,665,666],[568,1077,1079],{"className":1078},[630,666],[568,1080,605],{"className":1081},[630,634,666],[568,1083,1086],{"className":1084},[1085],"vlist-s","​",[568,1088,1090],{"className":1089},[646],[568,1091,1094],{"className":1092,"style":1093},[650],"height:0.345em;",[568,1095],{},[568,1097],{"className":1098},[789,1025],[568,1100,1102],{"className":1101,"style":1001},[789,1000],[568,1103,747],{"className":1104},[1005,1006],[568,1106,1108],{"className":1107},[638],[568,1109,1111],{"className":1110},[642],[568,1112,1114],{"className":1113},[646],[568,1115,1118],{"className":1116,"style":1117},[650],"height:1.0841em;",[568,1119,1121,1124],{"style":1120},"top:-3.333em;margin-right:0.05em;",[568,1122],{"className":1123,"style":659},[658],[568,1125,1127],{"className":1126},[663,664,665,666],[568,1128,596],{"className":1129},[630,666],[568,1131],{"className":1132,"style":674},[673],[568,1134,600],{"className":1135},[678],[568,1137],{"className":1138,"style":674},[673],[568,1140,1142,1146,1215],{"className":1141},[621],[568,1143],{"className":1144,"style":1145},[625],"height:1.1901em;vertical-align:-0.345em;",[568,1147,1149,1152,1212],{"className":1148},[630],[568,1150],{"className":1151},[764,1025],[568,1153,1155],{"className":1154},[841],[568,1156,1158,1204],{"className":1157},[642,1032],[568,1159,1161,1201],{"className":1160},[646],[568,1162,1165,1179,1187],{"className":1163,"style":1164},[650],"height:0.8451em;",[568,1166,1167,1170],{"style":1042},[568,1168],{"className":1169,"style":1046},[658],[568,1171,1173],{"className":1172},[663,664,665,666],[568,1174,1176],{"className":1175},[630,666],[568,1177,860],{"className":1178},[630,666],[568,1180,1181,1184],{"style":1058},[568,1182],{"className":1183,"style":1046},[658],[568,1185],{"className":1186,"style":1066},[1065],[568,1188,1189,1192],{"style":1069},[568,1190],{"className":1191,"style":1046},[658],[568,1193,1195],{"className":1194},[663,664,665,666],[568,1196,1198],{"className":1197},[630,666],[568,1199,857],{"className":1200},[630,666],[568,1202,1086],{"className":1203},[1085],[568,1205,1207],{"className":1206},[646],[568,1208,1210],{"className":1209,"style":1093},[650],[568,1211],{},[568,1213],{"className":1214},[789,1025],[568,1216,1218,1221],{"className":1217},[630],[568,1219,605],{"className":1220},[630,634],[568,1222,1224],{"className":1223},[638],[568,1225,1227],{"className":1226},[642],[568,1228,1230],{"className":1229},[646],[568,1231,1233],{"className":1232,"style":651},[650],[568,1234,1235,1238],{"style":654},[568,1236],{"className":1237,"style":659},[658],[568,1239,1241],{"className":1240},[663,664,665,666],[568,1242,596],{"className":1243},[630,666]," ist nur für ",[568,1246,1248,1271],{"className":1247},[571],[568,1249,1251],{"className":1250},[575],[577,1252,1253],{"xmlns":579},[581,1254,1255,1268],{},[584,1256,1257,1259,1261,1263,1265],{},[590,1258,592],{},[598,1260,829],{},[590,1262,605],{},[598,1264,829],{},[594,1266,1267],{},"0",[609,1269,1270],{"encoding":611},"a = b = 0",[568,1272,1274,1293,1312],{"className":1273,"ariaHidden":617},[616],[568,1275,1277,1281,1284,1287,1290],{"className":1276},[621],[568,1278],{"className":1279,"style":1280},[625],"height:0.4306em;",[568,1282,592],{"className":1283},[630,634],[568,1285],{"className":1286,"style":975},[673],[568,1288,829],{"className":1289},[979],[568,1291],{"className":1292,"style":975},[673],[568,1294,1296,1300,1303,1306,1309],{"className":1295},[621],[568,1297],{"className":1298,"style":1299},[625],"height:0.6944em;",[568,1301,605],{"className":1302},[630,634],[568,1304],{"className":1305,"style":975},[673],[568,1307,829],{"className":1308},[979],[568,1310],{"className":1311,"style":975},[673],[568,1313,1315,1319],{"className":1314},[621],[568,1316],{"className":1317,"style":1318},[625],"height:0.6444em;",[568,1320,1267],{"className":1321},[630]," gleich null. Die Gleichung ",[568,1324,1326,1357],{"className":1325},[571],[568,1327,1329],{"className":1328},[575],[577,1330,1331],{"xmlns":579},[581,1332,1333,1354],{},[584,1334,1335,1342,1344,1350,1352],{},[587,1336,1337,1340],{},[590,1338,1339],{},"x",[594,1341,857],{},[598,1343,600],{},[587,1345,1346,1348],{},[590,1347,605],{},[594,1349,857],{},[598,1351,829],{},[594,1353,1267],{},[609,1355,1356],{"encoding":611},"x^3 + b^3 = 0",[568,1358,1360,1404,1448],{"className":1359,"ariaHidden":617},[616],[568,1361,1363,1366,1395,1398,1401],{"className":1362},[621],[568,1364],{"className":1365,"style":626},[625],[568,1367,1369,1372],{"className":1368},[630],[568,1370,1339],{"className":1371},[630,634],[568,1373,1375],{"className":1374},[638],[568,1376,1378],{"className":1377},[642],[568,1379,1381],{"className":1380},[646],[568,1382,1384],{"className":1383,"style":651},[650],[568,1385,1386,1389],{"style":654},[568,1387],{"className":1388,"style":659},[658],[568,1390,1392],{"className":1391},[663,664,665,666],[568,1393,857],{"className":1394},[630,666],[568,1396],{"className":1397,"style":674},[673],[568,1399,600],{"className":1400},[678],[568,1402],{"className":1403,"style":674},[673],[568,1405,1407,1410,1439,1442,1445],{"className":1406},[621],[568,1408],{"className":1409,"style":651},[625],[568,1411,1413,1416],{"className":1412},[630],[568,1414,605],{"className":1415},[630,634],[568,1417,1419],{"className":1418},[638],[568,1420,1422],{"className":1421},[642],[568,1423,1425],{"className":1424},[646],[568,1426,1428],{"className":1427,"style":651},[650],[568,1429,1430,1433],{"style":654},[568,1431],{"className":1432,"style":659},[658],[568,1434,1436],{"className":1435},[663,664,665,666],[568,1437,857],{"className":1438},[630,666],[568,1440],{"className":1441,"style":975},[673],[568,1443,829],{"className":1444},[979],[568,1446],{"className":1447,"style":975},[673],[568,1449,1451,1454],{"className":1450},[621],[568,1452],{"className":1453,"style":1318},[625],[568,1455,1267],{"className":1456},[630]," hat deshalb nur die reelle Lösung ",[568,1459,1461,1481],{"className":1460},[571],[568,1462,1464],{"className":1463},[575],[577,1465,1466],{"xmlns":579},[581,1467,1468,1478],{},[584,1469,1470,1472,1474,1476],{},[590,1471,1339],{},[598,1473,829],{},[598,1475,814],{},[590,1477,605],{},[609,1479,1480],{"encoding":611},"x = -b",[568,1482,1484,1502],{"className":1483,"ariaHidden":617},[616],[568,1485,1487,1490,1493,1496,1499],{"className":1486},[621],[568,1488],{"className":1489,"style":1280},[625],[568,1491,1339],{"className":1492},[630,634],[568,1494],{"className":1495,"style":975},[673],[568,1497,829],{"className":1498},[979],[568,1500],{"className":1501,"style":975},[673],[568,1503,1505,1508,1511],{"className":1504},[621],[568,1506],{"className":1507,"style":923},[625],[568,1509,814],{"className":1510},[630],[568,1512,605],{"className":1513},[630,634],".",[564,1516,1517,1518,1546,1547,1581],{},"Die Formel entsteht aus der Differenz dritter Potenzen, wenn man dort ",[568,1519,1521,1534],{"className":1520},[571],[568,1522,1524],{"className":1523},[575],[577,1525,1526],{"xmlns":579},[581,1527,1528,1532],{},[584,1529,1530],{},[590,1531,605],{},[609,1533,605],{"encoding":611},[568,1535,1537],{"className":1536,"ariaHidden":617},[616],[568,1538,1540,1543],{"className":1539},[621],[568,1541],{"className":1542,"style":1299},[625],[568,1544,605],{"className":1545},[630,634]," durch ",[568,1548,1550,1566],{"className":1549},[571],[568,1551,1553],{"className":1552},[575],[577,1554,1555],{"xmlns":579},[581,1556,1557,1563],{},[584,1558,1559,1561],{},[598,1560,814],{},[590,1562,605],{},[609,1564,1565],{"encoding":611},"-b",[568,1567,1569],{"className":1568,"ariaHidden":617},[616],[568,1570,1572,1575,1578],{"className":1571},[621],[568,1573],{"className":1574,"style":923},[625],[568,1576,814],{"className":1577},[630],[568,1579,605],{"className":1580},[630,634]," ersetzt.",[559,1583,1585],{"id":1584},"herleitung","Herleitung",[564,1587,1588],{},"Ausmultiplizieren der rechten Seite:",[568,1590,1593],{"className":1591},[1592],"katex-display",[568,1594,1596,1715],{"className":1595},[571],[568,1597,1599],{"className":1598},[575],[577,1600,1602],{"xmlns":579,"display":1601},"block",[581,1603,1604,1712],{},[584,1605,1606,1608,1610,1612,1614,1616,1618,1624,1626,1628,1630,1632,1638,1640,1642,1648,1650,1656,1658,1660,1662,1668,1670,1676,1678,1680,1682,1688,1690,1696,1698,1704,1706],{},[598,1607,738],{"stretchy":737},[590,1609,592],{},[598,1611,600],{},[590,1613,605],{},[598,1615,747],{"stretchy":737},[598,1617,738],{"stretchy":737},[587,1619,1620,1622],{},[590,1621,592],{},[594,1623,596],{},[598,1625,814],{},[590,1627,592],{},[590,1629,605],{},[598,1631,600],{},[587,1633,1634,1636],{},[590,1635,605],{},[594,1637,596],{},[598,1639,747],{"stretchy":737},[598,1641,829],{},[587,1643,1644,1646],{},[590,1645,592],{},[594,1647,857],{},[598,1649,814],{},[587,1651,1652,1654],{},[590,1653,592],{},[594,1655,596],{},[590,1657,605],{},[598,1659,600],{},[590,1661,592],{},[587,1663,1664,1666],{},[590,1665,605],{},[594,1667,596],{},[598,1669,600],{},[587,1671,1672,1674],{},[590,1673,592],{},[594,1675,596],{},[590,1677,605],{},[598,1679,814],{},[590,1681,592],{},[587,1683,1684,1686],{},[590,1685,605],{},[594,1687,596],{},[598,1689,600],{},[587,1691,1692,1694],{},[590,1693,605],{},[594,1695,857],{},[598,1697,829],{},[587,1699,1700,1702],{},[590,1701,592],{},[594,1703,857],{},[598,1705,600],{},[587,1707,1708,1710],{},[590,1709,605],{},[594,1711,857],{},[609,1713,1714],{"encoding":611},"(a + b)(a^2 - ab + b^2) = a^3 - a^2b + ab^2 + a^2b - ab^2 + b^3 = a^3 + 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+ 27 = x^3 + 3^3 = (x + 3)(x^2 - 3x + 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+ 1 = (2y)^3 + 1^3 = (2y + 1)(4y^2 - 2y + 1)",[568,2651,2653,2702,2720,2773,2817,2841,2897,2919],{"className":2652,"ariaHidden":617},[616],[568,2654,2656,2660,2663,2693,2696,2699],{"className":2655},[621],[568,2657],{"className":2658,"style":2659},[625],"height:1.0585em;vertical-align:-0.1944em;",[568,2661,2576],{"className":2662},[630],[568,2664,2666,2670],{"className":2665},[630],[568,2667,2581],{"className":2668,"style":2669},[630,634],"margin-right:0.0359em;",[568,2671,2673],{"className":2672},[638],[568,2674,2676],{"className":2675},[642],[568,2677,2679],{"className":2678},[646],[568,2680,2682],{"className":2681,"style":1773},[650],[568,2683,2684,2687],{"style":1776},[568,2685],{"className":2686,"style":659},[658],[568,2688,2690],{"className":2689},[663,664,665,666],[568,2691,857],{"className":2692},[630,666],[568,2694],{"className":2695,"style":674},[673],[568,2697,600],{"className":2698},[678],[568,2700],{"className":2701,"style":674},[673],[568,2703,2705,2708,2711,2714,2717],{"className":2704},[621],[568,2706],{"className":2707,"style":1318},[625],[568,2709,2588],{"className":2710},[630],[568,2712],{"className":2713,"style":975},[673],[568,2715,829],{"className":2716},[979],[568,2718],{"className":2719,"style":975},[673],[568,2721,2723,2726,2729,2732,2735,2764,2767,2770],{"className":2722},[621],[568,2724],{"className":2725,"style":1745},[625],[568,2727,738],{"className":2728},[764],[568,2730,596],{"className":2731},[630],[568,2733,2581],{"className":2734,"style":2669},[630,634],[568,2736,2738,2741],{"className":2737},[789],[568,2739,747],{"className":2740},[789],[568,2742,2744],{"className":2743},[638],[568,2745,2747],{"className":2746},[642],[568,2748,2750],{"className":2749},[646],[568,2751,2753],{"className":2752,"style":1773},[650],[568,2754,2755,2758],{"style":1776},[568,2756],{"className":2757,"style":659},[658],[568,2759,2761],{"className":2760},[663,664,665,666],[568,2762,857],{"className":2763},[630,666],[568,2765],{"className":2766,"style":674},[673],[568,2768,600],{"className":2769},[678],[568,2771],{"className":2772,"style":674},[673],[568,2774,2776,2779,2808,2811,2814],{"className":2775},[621],[568,2777],{"className":2778,"style":1773},[625],[568,2780,2782,2785],{"className":2781},[630],[568,2783,2588],{"className":2784},[630],[568,2786,2788],{"className":2787},[638],[568,2789,2791],{"className":2790},[642],[568,2792,2794],{"className":2793},[646],[568,2795,2797],{"className":2796,"style":1773},[650],[568,2798,2799,2802],{"style":1776},[568,2800],{"className":2801,"style":659},[658],[568,2803,2805],{"className":2804},[663,664,665,666],[568,2806,857],{"className":2807},[630,666],[568,2809],{"className":2810,"style":975},[673],[568,2812,829],{"className":2813},[979],[568,2815],{"className":2816,"style":975},[673],[568,2818,2820,2823,2826,2829,2832,2835,2838],{"className":2819},[621],[568,2821],{"className":2822,"style":760},[625],[568,2824,738],{"className":2825},[764],[568,2827,596],{"className":2828},[630],[568,2830,2581],{"className":2831,"style":2669},[630,634],[568,2833],{"className":2834,"style":674},[673],[568,2836,600],{"className":2837},[678],[568,2839],{"className":2840,"style":674},[673],[568,2842,2844,2847,2850,2853,2856,2859,2888,2891,2894],{"className":2843},[621],[568,2845],{"className":2846,"style":1745},[625],[568,2848,2588],{"className":2849},[630],[568,2851,747],{"className":2852},[789],[568,2854,738],{"className":2855},[764],[568,2857,860],{"className":2858},[630],[568,2860,2862,2865],{"className":2861},[630],[568,2863,2581],{"className":2864,"style":2669},[630,634],[568,2866,2868],{"className":2867},[638],[568,2869,2871],{"className":2870},[642],[568,2872,2874],{"className":2873},[646],[568,2875,2877],{"className":2876,"style":1773},[650],[568,2878,2879,2882],{"style":1776},[568,2880],{"className":2881,"style":659},[658],[568,2883,2885],{"className":2884},[663,664,665,666],[568,2886,596],{"className":2887},[630,666],[568,2889],{"className":2890,"style":674},[673],[568,2892,814],{"className":2893},[678],[568,2895],{"className":2896,"style":674},[673],[568,2898,2900,2904,2907,2910,2913,2916],{"className":2899},[621],[568,2901],{"className":2902,"style":2903},[625],"height:0.8389em;vertical-align:-0.1944em;",[568,2905,596],{"className":2906},[630],[568,2908,2581],{"className":2909,"style":2669},[630,634],[568,2911],{"className":2912,"style":674},[673],[568,2914,600],{"className":2915},[678],[568,2917],{"className":2918,"style":674},[673],[568,2920,2922,2925,2928],{"className":2921},[621],[568,2923],{"className":2924,"style":760},[625],[568,2926,2588],{"className":2927},[630],[568,2929,747],{"className":2930},[789],[564,2932,2933,2934,3182,3183,1514],{},"Gleichung: ",[568,2935,2937,2993],{"className":2936},[571],[568,2938,2940],{"className":2939},[575],[577,2941,2942],{"xmlns":579},[581,2943,2944,2990],{},[584,2945,2946,2952,2954,2956,2958,2960,2962,2964,2966,2968,2970,2976,2978,2980,2982,2984,2986,2988],{},[587,2947,2948,2950],{},[590,2949,1339],{},[594,2951,857],{},[598,2953,600],{},[594,2955,2588],{},[598,2957,829],{},[598,2959,738],{"stretchy":737},[590,2961,1339],{},[598,2963,600],{},[594,2965,2588],{},[598,2967,747],{"stretchy":737},[598,2969,738],{"stretchy":737},[587,2971,2972,2974],{},[590,2973,1339],{},[594,2975,596],{},[598,2977,814],{},[590,2979,1339],{},[598,2981,600],{},[594,2983,2588],{},[598,2985,747],{"stretchy":737},[598,2987,829],{},[594,2989,1267],{},[609,2991,2992],{"encoding":611},"x^3 + 1 = (x + 1)(x^2 - x + 1) = 0",[568,2994,2996,3040,3058,3079,3133,3152,3173],{"className":2995,"ariaHidden":617},[616],[568,2997,2999,3002,3031,3034,3037],{"className":2998},[621],[568,3000],{"className":3001,"style":626},[625],[568,3003,3005,3008],{"className":3004},[630],[568,3006,1339],{"className":3007},[630,634],[568,3009,3011],{"className":3010},[638],[568,3012,3014],{"className":3013},[642],[568,3015,3017],{"className":3016},[646],[568,3018,3020],{"className":3019,"style":651},[650],[568,3021,3022,3025],{"style":654},[568,3023],{"className":3024,"style":659},[658],[568,3026,3028],{"className":3027},[663,664,665,666],[568,3029,857],{"className":3030},[630,666],[568,3032],{"className":3033,"style":674},[673],[568,3035,600],{"className":3036},[678],[568,3038],{"className":3039,"style":674},[673],[568,3041,3043,3046,3049,3052,3055],{"className":3042},[621],[568,3044],{"className":3045,"style":1318},[625],[568,3047,2588],{"className":3048},[630],[568,3050],{"className":3051,"style":975},[673],[568,3053,829],{"className":3054},[979],[568,3056],{"className":3057,"style":975},[673],[568,3059,3061,3064,3067,3070,3073,3076],{"className":3060},[621],[568,3062],{"className":3063,"style":760},[625],[568,3065,738],{"className":3066},[764],[568,3068,1339],{"className":3069},[630,634],[568,3071],{"className":3072,"style":674},[673],[568,3074,600],{"className":3075},[678],[568,3077],{"className":3078,"style":674},[673],[568,3080,3082,3086,3089,3092,3095,3124,3127,3130],{"className":3081},[621],[568,3083],{"className":3084,"style":3085},[625],"height:1.0641em;vertical-align:-0.25em;",[568,3087,2588],{"className":3088},[630],[568,3090,747],{"className":3091},[789],[568,3093,738],{"className":3094},[764],[568,3096,3098,3101],{"className":3097},[630],[568,3099,1339],{"className":3100},[630,634],[568,3102,3104],{"className":3103},[638],[568,3105,3107],{"className":3106},[642],[568,3108,3110],{"className":3109},[646],[568,3111,3113],{"className":3112,"style":651},[650],[568,3114,3115,3118],{"style":654},[568,3116],{"className":3117,"style":659},[658],[568,3119,3121],{"className":3120},[663,664,665,666],[568,3122,596],{"className":3123},[630,666],[568,3125],{"className":3126,"style":674},[673],[568,3128,814],{"className":3129},[678],[568,3131],{"className":3132,"style":674},[673],[568,3134,3136,3140,3143,3146,3149],{"className":3135},[621],[568,3137],{"className":3138,"style":3139},[625],"height:0.6667em;vertical-align:-0.0833em;",[568,3141,1339],{"className":3142},[630,634],[568,3144],{"className":3145,"style":674},[673],[568,3147,600],{"className":3148},[678],[568,3150],{"className":3151,"style":674},[673],[568,3153,3155,3158,3161,3164,3167,3170],{"className":3154},[621],[568,3156],{"className":3157,"style":760},[625],[568,3159,2588],{"className":3160},[630],[568,3162,747],{"className":3163},[789],[568,3165],{"className":3166,"style":975},[673],[568,3168,829],{"className":3169},[979],[568,3171],{"className":3172,"style":975},[673],[568,3174,3176,3179],{"className":3175},[621],[568,3177],{"className":3178,"style":1318},[625],[568,3180,1267],{"className":3181},[630]," hat nur die reelle Lösung ",[568,3184,3186,3206],{"className":3185},[571],[568,3187,3189],{"className":3188},[575],[577,3190,3191],{"xmlns":579},[581,3192,3193,3203],{},[584,3194,3195,3197,3199,3201],{},[590,3196,1339],{},[598,3198,829],{},[598,3200,814],{},[594,3202,2588],{},[609,3204,3205],{"encoding":611},"x = -1",[568,3207,3209,3227],{"className":3208,"ariaHidden":617},[616],[568,3210,3212,3215,3218,3221,3224],{"className":3211},[621],[568,3213],{"className":3214,"style":1280},[625],[568,3216,1339],{"className":3217},[630,634],[568,3219],{"className":3220,"style":975},[673],[568,3222,829],{"className":3223},[979],[568,3225],{"className":3226,"style":975},[673],[568,3228,3230,3233,3236],{"className":3229},[621],[568,3231],{"className":3232,"style":2531},[625],[568,3234,814],{"className":3235},[630],[568,3237,2588],{"className":3238},[630],[564,3240,3241],{},"Kopfrechnen:",[568,3243,3245],{"className":3244},[1592],[568,3246,3248,3320],{"className":3247},[571],[568,3249,3251],{"className":3250},[575],[577,3252,3253],{"xmlns":579,"display":1601},[581,3254,3255,3317],{},[584,3256,3257,3263,3265,3272,3274,3276,3278,3280,3282,3284,3286,3289,3291,3294,3296,3299,3301,3303,3306,3309,3312,3314],{},[587,3258,3259,3261],{},[594,3260,860],{},[594,3262,857],{},[598,3264,600],{},[587,3266,3267,3270],{},[594,3268,3269],{},"6",[594,3271,857],{},[598,3273,829],{},[598,3275,738],{"stretchy":737},[594,3277,860],{},[598,3279,600],{},[594,3281,3269],{},[598,3283,747],{"stretchy":737},[598,3285,738],{"stretchy":737},[594,3287,3288],{},"16",[598,3290,814],{},[594,3292,3293],{},"24",[598,3295,600],{},[594,3297,3298],{},"36",[598,3300,747],{"stretchy":737},[598,3302,829],{},[594,3304,3305],{},"10",[598,3307,3308],{},"⋅",[594,3310,3311],{},"28",[598,3313,829],{},[594,3315,3316],{},"280",[609,3318,3319],{"encoding":611},"4^3 + 6^3 = (4 + 6)(16 - 24 + 36) = 10 \\cdot 28 = 280",[568,3321,3323,3367,3411,3432,3459,3477,3498,3516,3534],{"className":3322,"ariaHidden":617},[616],[568,3324,3326,3329,3358,3361,3364],{"className":3325},[621],[568,3327],{"className":3328,"style":1866},[625],[568,3330,3332,3335],{"className":3331},[630],[568,3333,860],{"className":3334},[630],[568,3336,3338],{"className":3337},[638],[568,3339,3341],{"className":3340},[642],[568,3342,3344],{"className":3343},[646],[568,3345,3347],{"className":3346,"style":1773},[650],[568,3348,3349,3352],{"style":1776},[568,3350],{"className":3351,"style":659},[658],[568,3353,3355],{"className":3354},[663,664,665,666],[568,3356,857],{"className":3357},[630,666],[568,3359],{"className":3360,"style":674},[673],[568,3362,600],{"className":3363},[678],[568,3365],{"className":3366,"style":674},[673],[568,3368,3370,3373,3402,3405,3408],{"className":3369},[621],[568,3371],{"className":3372,"style":1773},[625],[568,3374,3376,3379],{"className":3375},[630],[568,3377,3269],{"className":3378},[630],[568,3380,3382],{"className":3381},[638],[568,3383,3385],{"className":3384},[642],[568,3386,3388],{"className":3387},[646],[568,3389,3391],{"className":3390,"style":1773},[650],[568,3392,3393,3396],{"style":1776},[568,3394],{"className":3395,"style":659},[658],[568,3397,3399],{"className":3398},[663,664,665,666],[568,3400,857],{"className":3401},[630,666],[568,3403],{"className":3404,"style":975},[673],[568,3406,829],{"className":3407},[979],[568,3409],{"className":3410,"style":975},[673],[568,3412,3414,3417,3420,3423,3426,3429],{"className":3413},[621],[568,3415],{"className":3416,"style":760},[625],[568,3418,738],{"className":3419},[764],[568,3421,860],{"className":3422},[630],[568,3424],{"className":3425,"style":674},[673],[568,3427,600],{"className":3428},[678],[568,3430],{"className":3431,"style":674},[673],[568,3433,3435,3438,3441,3444,3447,3450,3453,3456],{"className":3434},[621],[568,3436],{"className":3437,"style":760},[625],[568,3439,3269],{"className":3440},[630],[568,3442,747],{"className":3443},[789],[568,3445,738],{"className":3446},[764],[568,3448,3288],{"className":3449},[630],[568,3451],{"className":3452,"style":674},[673],[568,3454,814],{"className":3455},[678],[568,3457],{"className":3458,"style":674},[673],[568,3460,3462,3465,3468,3471,3474],{"className":3461},[621],[568,3463],{"className":3464,"style":2531},[625],[568,3466,3293],{"className":3467},[630],[568,3469],{"className":3470,"style":674},[673],[568,3472,600],{"className":3473},[678],[568,3475],{"className":3476,"style":674},[673],[568,3478,3480,3483,3486,3489,3492,3495],{"className":3479},[621],[568,3481],{"className":3482,"style":760},[625],[568,3484,3298],{"className":3485},[630],[568,3487,747],{"className":3488},[789],[568,3490],{"className":3491,"style":975},[673],[568,3493,829],{"className":3494},[979],[568,3496],{"className":3497,"style":975},[673],[568,3499,3501,3504,3507,3510,3513],{"className":3500},[621],[568,3502],{"className":3503,"style":1318},[625],[568,3505,3305],{"className":3506},[630],[568,3508],{"className":3509,"style":674},[673],[568,3511,3308],{"className":3512},[678],[568,3514],{"className":3515,"style":674},[673],[568,3517,3519,3522,3525,3528,3531],{"className":3518},[621],[568,3520],{"className":3521,"style":1318},[625],[568,3523,3311],{"className":3524},[630],[568,3526],{"className":3527,"style":975},[673],[568,3529,829],{"className":3530},[979],[568,3532],{"className":3533,"style":975},[673],[568,3535,3537,3540],{"className":3536},[621],[568,3538],{"className":3539,"style":1318},[625],[568,3541,3316],{"className":3542},[630],[559,3544,3546],{"id":3545},"typische-fehler","Typische Fehler",[3548,3549,3550,4004,4148],"ul",{},[3551,3552,3553,3644,3645,3756,3757,3870,3871,1514],"li",{},[568,3554,3556,3582],{"className":3555},[571],[568,3557,3559],{"className":3558},[575],[577,3560,3561],{"xmlns":579},[581,3562,3563,3579],{},[584,3564,3565,3567,3569,3571,3573],{},[598,3566,738],{"stretchy":737},[590,3568,592],{},[598,3570,600],{},[590,3572,605],{},[587,3574,3575,3577],{},[598,3576,747],{"stretchy":737},[594,3578,857],{},[609,3580,3581],{"encoding":611},"(a + b)^3",[568,3583,3585,3606],{"className":3584,"ariaHidden":617},[616],[568,3586,3588,3591,3594,3597,3600,3603],{"className":3587},[621],[568,3589],{"className":3590,"style":760},[625],[568,3592,738],{"className":3593},[764],[568,3595,592],{"className":3596},[630,634],[568,3598],{"className":3599,"style":674},[673],[568,3601,600],{"className":3602},[678],[568,3604],{"className":3605,"style":674},[673],[568,3607,3609,3612,3615],{"className":3608},[621],[568,3610],{"className":3611,"style":3085},[625],[568,3613,605],{"className":3614},[630,634],[568,3616,3618,3621],{"className":3617},[789],[568,3619,747],{"className":3620},[789],[568,3622,3624],{"className":3623},[638],[568,3625,3627],{"className":3626},[642],[568,3628,3630],{"className":3629},[646],[568,3631,3633],{"className":3632,"style":651},[650],[568,3634,3635,3638],{"style":654},[568,3636],{"className":3637,"style":659},[658],[568,3639,3641],{"className":3640},[663,664,665,666],[568,3642,857],{"className":3643},[630,666]," mit ",[568,3646,3648,3674],{"className":3647},[571],[568,3649,3651],{"className":3650},[575],[577,3652,3653],{"xmlns":579},[581,3654,3655,3671],{},[584,3656,3657,3663,3665],{},[587,3658,3659,3661],{},[590,3660,592],{},[594,3662,857],{},[598,3664,600],{},[587,3666,3667,3669],{},[590,3668,605],{},[594,3670,857],{},[609,3672,3673],{"encoding":611},"a^3 + b^3",[568,3675,3677,3721],{"className":3676,"ariaHidden":617},[616],[568,3678,3680,3683,3712,3715,3718],{"className":3679},[621],[568,3681],{"className":3682,"style":626},[625],[568,3684,3686,3689],{"className":3685},[630],[568,3687,592],{"className":3688},[630,634],[568,3690,3692],{"className":3691},[638],[568,3693,3695],{"className":3694},[642],[568,3696,3698],{"className":3697},[646],[568,3699,3701],{"className":3700,"style":651},[650],[568,3702,3703,3706],{"style":654},[568,3704],{"className":3705,"style":659},[658],[568,3707,3709],{"className":3708},[663,664,665,666],[568,3710,857],{"className":3711},[630,666],[568,3713],{"className":3714,"style":674},[673],[568,3716,600],{"className":3717},[678],[568,3719],{"className":3720,"style":674},[673],[568,3722,3724,3727],{"className":3723},[621],[568,3725],{"className":3726,"style":651},[625],[568,3728,3730,3733],{"className":3729},[630],[568,3731,605],{"className":3732},[630,634],[568,3734,3736],{"className":3735},[638],[568,3737,3739],{"className":3738},[642],[568,3740,3742],{"className":3741},[646],[568,3743,3745],{"className":3744,"style":651},[650],[568,3746,3747,3750],{"style":654},[568,3748],{"className":3749,"style":659},[658],[568,3751,3753],{"className":3752},[663,664,665,666],[568,3754,857],{"className":3755},[630,666]," verwechseln: ",[568,3758,3760,3790],{"className":3759},[571],[568,3761,3763],{"className":3762},[575],[577,3764,3765],{"xmlns":579},[581,3766,3767,3787],{},[584,3768,3769,3771,3773,3775,3777,3783,3785],{},[598,3770,738],{"stretchy":737},[594,3772,2588],{},[598,3774,600],{},[594,3776,596],{},[587,3778,3779,3781],{},[598,3780,747],{"stretchy":737},[594,3782,857],{},[598,3784,829],{},[594,3786,2245],{},[609,3788,3789],{"encoding":611},"(1 + 2)^3 = 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aber ",[568,3872,3874,3904],{"className":3873},[571],[568,3875,3877],{"className":3876},[575],[577,3878,3879],{"xmlns":579},[581,3880,3881,3901],{},[584,3882,3883,3889,3891,3897,3899],{},[587,3884,3885,3887],{},[594,3886,2588],{},[594,3888,857],{},[598,3890,600],{},[587,3892,3893,3895],{},[594,3894,596],{},[594,3896,857],{},[598,3898,829],{},[594,3900,2292],{},[609,3902,3903],{"encoding":611},"1^3 + 2^3 = 9",[568,3905,3907,3951,3995],{"className":3906,"ariaHidden":617},[616],[568,3908,3910,3913,3942,3945,3948],{"className":3909},[621],[568,3911],{"className":3912,"style":626},[625],[568,3914,3916,3919],{"className":3915},[630],[568,3917,2588],{"className":3918},[630],[568,3920,3922],{"className":3921},[638],[568,3923,3925],{"className":3924},[642],[568,3926,3928],{"className":3927},[646],[568,3929,3931],{"className":3930,"style":651},[650],[568,3932,3933,3936],{"style":654},[568,3934],{"className":3935,"style":659},[658],[568,3937,3939],{"className":3938},[663,664,665,666],[568,3940,857],{"className":3941},[630,666],[568,3943],{"className":3944,"style":674},[673],[568,3946,600],{"className":3947},[678],[568,3949],{"className":3950,"style":674},[673],[568,3952,3954,3957,3986,3989,3992],{"className":3953},[621],[568,3955],{"className":3956,"style":651},[625],[568,3958,3960,3963],{"className":3959},[630],[568,3961,596],{"className":3962},[630],[568,3964,3966],{"className":3965},[638],[568,3967,3969],{"className":3968},[642],[568,3970,3972],{"className":3971},[646],[568,3973,3975],{"className":3974,"style":651},[650],[568,3976,3977,3980],{"style":654},[568,3978],{"className":3979,"style":659},[658],[568,3981,3983],{"className":3982},[663,664,665,666],[568,3984,857],{"className":3985},[630,666],[568,3987],{"className":3988,"style":975},[673],[568,3990,829],{"className":3991},[979],[568,3993],{"className":3994,"style":975},[673],[568,3996,3998,4001],{"className":3997},[621],[568,3999],{"className":4000,"style":1318},[625],[568,4002,2292],{"className":4003},[630],[3551,4005,4006,4007,4043,4044,4080,4081,4116,4117,4147],{},"Im zweiten Faktor ",[568,4008,4010,4028],{"className":4009},[571],[568,4011,4013],{"className":4012},[575],[577,4014,4015],{"xmlns":579},[581,4016,4017,4025],{},[584,4018,4019,4021,4023],{},[598,4020,600],{},[590,4022,592],{},[590,4024,605],{},[609,4026,4027],{"encoding":611},"+ab",[568,4029,4031],{"className":4030,"ariaHidden":617},[616],[568,4032,4034,4037,4040],{"className":4033},[621],[568,4035],{"className":4036,"style":923},[625],[568,4038,600],{"className":4039},[630],[568,4041,927],{"className":4042},[630,634]," schreiben. Bei der Summe steht ",[568,4045,4047,4065],{"className":4046},[571],[568,4048,4050],{"className":4049},[575],[577,4051,4052],{"xmlns":579},[581,4053,4054,4062],{},[584,4055,4056,4058,4060],{},[598,4057,814],{},[590,4059,592],{},[590,4061,605],{},[609,4063,4064],{"encoding":611},"-ab",[568,4066,4068],{"className":4067,"ariaHidden":617},[616],[568,4069,4071,4074,4077],{"className":4070},[621],[568,4072],{"className":4073,"style":923},[625],[568,4075,814],{"className":4076},[630],[568,4078,927],{"className":4079},[630,634],", bei der Differenz ",[568,4082,4084,4101],{"className":4083},[571],[568,4085,4087],{"className":4086},[575],[577,4088,4089],{"xmlns":579},[581,4090,4091,4099],{},[584,4092,4093,4095,4097],{},[598,4094,600],{},[590,4096,592],{},[590,4098,605],{},[609,4100,4027],{"encoding":611},[568,4102,4104],{"className":4103,"ariaHidden":617},[616],[568,4105,4107,4110,4113],{"className":4106},[621],[568,4108],{"className":4109,"style":923},[625],[568,4111,600],{"className":4112},[630],[568,4114,927],{"className":4115},[630,634],". Merkhilfe: Das Vorzeichen im ersten Faktor ist dasselbe wie in der Aufgabe, das von ",[568,4118,4120,4135],{"className":4119},[571],[568,4121,4123],{"className":4122},[575],[577,4124,4125],{"xmlns":579},[581,4126,4127,4133],{},[584,4128,4129,4131],{},[590,4130,592],{},[590,4132,605],{},[609,4134,927],{"encoding":611},[568,4136,4138],{"className":4137,"ariaHidden":617},[616],[568,4139,4141,4144],{"className":4140},[621],[568,4142],{"className":4143,"style":1299},[625],[568,4145,927],{"className":4146},[630,634]," ist das entgegengesetzte.",[3551,4149,4150,4151,4261,4262,4372],{},"Annehmen, dass sich 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wie 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nicht zerlegen lässt.",{"title":4374,"searchDepth":4375,"depth":4375,"links":4376},"",2,[4377,4378,4379,4380],{"id":561,"depth":4375,"text":562},{"id":1584,"depth":4375,"text":1585},{"id":2218,"depth":4375,"text":2219},{"id":3545,"depth":4375,"text":3546},[4382,4384,4387,4390,4394,4397,4399,4402,4404],{"lhs":3673,"rhs":4383},"(a + b) * (a^2 - a*b + b^2)",{"lhs":4385,"rhs":4386},"x^3 + 27","(x + 3) * (x^2 - 3*x + 9)",{"lhs":4388,"rhs":4389},"8*y^3 + 1","(2*y + 1) * (4*y^2 - 2*y + 1)",{"lhs":4391,"rhs":1267,"where":4392},"x^3 + 1",{"x":4393},-1,{"lhs":4395,"rhs":4396},"4^3 + 6^3","(4 + 6) * (16 - 24 + 36)",{"lhs":4398,"rhs":3316},"64 + 216",{"lhs":4400,"rhs":4401},"a^2 - a*b + b^2","(a - b\u002F2)^2 + 3*b^2\u002F4",{"lhs":4403,"rhs":2245},"(1 + 2)^3",{"lhs":4405,"rhs":2292},"1^3 + 2^3",null,"md","sum-of-cubes-factoring","a^3 + b^3 = (a + b)(a^2 - ab + b^2)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a^3 + b^3 = (a + b)(a^2 - ab + 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