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des gemeinsamen Faktors ",[572,1065,1067,1080],{"className":1066},[575],[572,1068,1070],{"className":1069},[579],[581,1071,1072],{"xmlns":583},[585,1073,1074,1078],{},[588,1075,1076],{},[820,1077,822],{},[632,1079,822],{"encoding":634},[572,1081,1083],{"className":1082,"ariaHidden":640},[639],[572,1084,1086,1089],{"className":1085},[644],[572,1087],{"className":1088,"style":926},[648],[572,1090,822],{"className":1091},[653],":",[572,1094,1096],{"className":1095},[805],[572,1097,1099,1137],{"className":1098},[575],[572,1100,1102],{"className":1101},[579],[581,1103,1104],{"xmlns":583,"display":814},[585,1105,1106,1134],{},[588,1107,1108,1111,1113,1115,1118,1120,1122,1124,1126,1128,1130,1132],{},[820,1109,1110],{},"6",[591,1112,827],{},[595,1114,830],{},[820,1116,1117],{},"9",[595,1119,616],{},[820,1121,822],{},[595,1123,601],{"stretchy":600},[820,1125,949],{},[591,1127,827],{},[595,1129,830],{},[820,1131,822],{},[595,1133,613],{"stretchy":600},[632,1135,1136],{"encoding":634},"6x + 9 = 3(2x + 3)",[572,1138,1140,1161,1179,1206],{"className":1139,"ariaHidden":640},[639],[572,1141,1143,1146,1149,1152,1155,1158],{"className":1142},[644],[572,1144],{"className":1145,"style":904},[648],[572,1147,1110],{"className":1148},[653],[572,1150,827],{"className":1151},[653,654],[572,1153],{"className":1154,"style":659},[658],[572,1156,830],{"className":1157},[663],[572,1159],{"className":1160,"style":659},[658],[572,1162,1164,1167,1170,1173,1176],{"className":1163},[644],[572,1165],{"className":1166,"style":926},[648],[572,1168,1117],{"className":1169},[653],[572,1171],{"className":1172,"style":706},[658],[572,1174,616],{"className":1175},[710],[572,1177],{"className":1178,"style":706},[658],[572,1180,1182,1185,1188,1191,1194,1197,1200,1203],{"className":1181},[644],[572,1183],{"className":1184,"style":673},[648],[572,1186,822],{"className":1187},[653],[572,1189,601],{"className":1190},[677],[572,1192,949],{"className":1193},[653],[572,1195,827],{"className":1196},[653,654],[572,1198],{"className":1199,"style":659},[658],[572,1201,830],{"className":1202},[663],[572,1204],{"className":1205,"style":659},[658],[572,1207,1209,1212,1215],{"className":1208},[644],[572,1210],{"className":1211,"style":673},[648],[572,1213,822],{"className":1214},[653],[572,1216,613],{"className":1217},[702],[563,1219,1220],{},"Kopfrechnen:",[572,1222,1224],{"className":1223},[805],[572,1225,1227,1269],{"className":1226},[575],[572,1228,1230],{"className":1229},[579],[581,1231,1232],{"xmlns":583,"display":814},[585,1233,1234,1266],{},[588,1235,1236,1239,1241,1244,1246,1248,1250,1253,1255,1257,1259,1261,1263],{},[820,1237,1238],{},"7",[595,1240,597],{},[820,1242,1243],{},"102",[595,1245,616],{},[820,1247,1238],{},[595,1249,597],{},[820,1251,1252],{},"100",[595,1254,830],{},[820,1256,1238],{},[595,1258,597],{},[820,1260,949],{},[595,1262,616],{},[820,1264,1265],{},"714",[632,1267,1268],{"encoding":634},"7 \\cdot 102 = 7 \\cdot 100 + 7 \\cdot 2 = 714",[572,1270,1272,1290,1308,1326,1344,1362,1380],{"className":1271,"ariaHidden":640},[639],[572,1273,1275,1278,1281,1284,1287],{"className":1274},[644],[572,1276],{"className":1277,"style":926},[648],[572,1279,1238],{"className":1280},[653],[572,1282],{"className":1283,"style":659},[658],[572,1285,597],{"className":1286},[663],[572,1288],{"className":1289,"style":659},[658],[572,1291,1293,1296,1299,1302,1305],{"className":1292},[644],[572,1294],{"className":1295,"style":926},[648],[572,1297,1243],{"className":1298},[653],[572,1300],{"className":1301,"style":706},[658],[572,1303,616],{"className":1304},[710],[572,1306],{"className":1307,"style":706},[658],[572,1309,1311,1314,1317,1320,1323],{"className":1310},[644],[572,1312],{"className":1313,"style":926},[648],[572,1315,1238],{"className":1316},[653],[572,1318],{"className":1319,"style":659},[658],[572,1321,597],{"className":1322},[663],[572,1324],{"className":1325,"style":659},[658],[572,1327,1329,1332,1335,1338,1341],{"className":1328},[644],[572,1330],{"className":1331,"style":904},[648],[572,1333,1252],{"className":1334},[653],[572,1336],{"className":1337,"style":659},[658],[572,1339,830],{"className":1340},[663],[572,1342],{"className":1343,"style":659},[658],[572,1345,1347,1350,1353,1356,1359],{"className":1346},[644],[572,1348],{"className":1349,"style":926},[648],[572,1351,1238],{"className":1352},[653],[572,1354],{"className":1355,"style":659},[658],[572,1357,597],{"className":1358},[663],[572,1360],{"className":1361,"style":659},[658],[572,1363,1365,1368,1371,1374,1377],{"className":1364},[644],[572,1366],{"className":1367,"style":926},[648],[572,1369,949],{"className":1370},[653],[572,1372],{"className":1373,"style":706},[658],[572,1375,616],{"className":1376},[710],[572,1378],{"className":1379,"style":706},[658],[572,1381,1383,1386],{"className":1382},[644],[572,1384],{"className":1385,"style":926},[648],[572,1387,1265],{"className":1388},[653],[558,1390,1392],{"id":1391},"typische-fehler","Typische Fehler",[784,1394,1395,1517,1653],{},[787,1396,1397,1398,1513,1514,779],{},"Nur den ersten Summanden multiplizieren: ",[572,1399,1401,1435],{"className":1400},[575],[572,1402,1404],{"className":1403},[579],[581,1405,1406],{"xmlns":583},[585,1407,1408,1432],{},[588,1409,1410,1412,1414,1416,1418,1420,1422,1424,1426,1428,1430],{},[820,1411,822],{},[595,1413,601],{"stretchy":600},[591,1415,827],{},[595,1417,830],{},[820,1419,833],{},[595,1421,613],{"stretchy":600},[595,1423,616],{},[820,1425,822],{},[591,1427,827],{},[595,1429,830],{},[820,1431,833],{},[632,1433,1434],{"encoding":634},"3(x+4) = 3x + 4",[572,1436,1438,1462,1483,1504],{"className":1437,"ariaHidden":640},[639],[572,1439,1441,1444,1447,1450,1453,1456,1459],{"className":1440},[644],[572,1442],{"className":1443,"style":673},[648],[572,1445,822],{"className":1446},[653],[572,1448,601],{"className":1449},[677],[572,1451,827],{"className":1452},[653,654],[572,1454],{"className":1455,"style":659},[658],[572,1457,830],{"className":1458},[663],[572,1460],{"className":1461,"style":659},[658],[572,1463,1465,1468,1471,1474,1477,1480],{"className":1464},[644],[572,1466],{"className":1467,"style":673},[648],[572,1469,833],{"className":1470},[653],[572,1472,613],{"className":1473},[702],[572,1475],{"className":1476,"style":706},[658],[572,1478,616],{"className":1479},[710],[572,1481],{"className":1482,"style":706},[658],[572,1484,1486,1489,1492,1495,1498,1501],{"className":1485},[644],[572,1487],{"className":1488,"style":904},[648],[572,1490,822],{"className":1491},[653],[572,1493,827],{"className":1494},[653,654],[572,1496],{"className":1497,"style":659},[658],[572,1499,830],{"className":1500},[663],[572,1502],{"className":1503,"style":659},[658],[572,1505,1507,1510],{"className":1506},[644],[572,1508],{"className":1509,"style":926},[648],[572,1511,833],{"className":1512},[653]," ist ",[567,1515,1516],{},"falsch",[787,1518,1519,1520,1618,1619,779],{},"Vorzeichen bei einem negativen Faktor: ",[572,1521,1523,1555],{"className":1522},[575],[572,1524,1526],{"className":1525},[579],[581,1527,1528],{"xmlns":583},[585,1529,1530,1552],{},[588,1531,1532,1534,1536,1538,1540,1542,1544,1546,1548,1550],{},[595,1533,607],{},[820,1535,949],{},[595,1537,597],{},[595,1539,601],{"stretchy":600},[595,1541,607],{},[820,1543,958],{},[595,1545,613],{"stretchy":600},[595,1547,616],{},[595,1549,830],{},[820,1551,973],{},[632,1553,1554],{"encoding":634},"-2 \\cdot (-5) = +10",[572,1556,1558,1579,1606],{"className":1557,"ariaHidden":640},[639],[572,1559,1561,1564,1567,1570,1573,1576],{"className":1560},[644],[572,1562],{"className":1563,"style":904},[648],[572,1565,607],{"className":1566},[653],[572,1568,949],{"className":1569},[653],[572,1571],{"className":1572,"style":659},[658],[572,1574,597],{"className":1575},[663],[572,1577],{"className":1578,"style":659},[658],[572,1580,1582,1585,1588,1591,1594,1597,1600,1603],{"className":1581},[644],[572,1583],{"className":1584,"style":673},[648],[572,1586,601],{"className":1587},[677],[572,1589,607],{"className":1590},[653],[572,1592,958],{"className":1593},[653],[572,1595,613],{"className":1596},[702],[572,1598],{"className":1599,"style":706},[658],[572,1601,616],{"className":1602},[710],[572,1604],{"className":1605,"style":706},[658],[572,1607,1609,1612,1615],{"className":1608},[644],[572,1610],{"className":1611,"style":904},[648],[572,1613,830],{"className":1614},[653],[572,1616,973],{"className":1617},[653],", nicht ",[572,1620,1622,1638],{"className":1621},[575],[572,1623,1625],{"className":1624},[579],[581,1626,1627],{"xmlns":583},[585,1628,1629,1635],{},[588,1630,1631,1633],{},[595,1632,607],{},[820,1634,973],{},[632,1636,1637],{"encoding":634},"-10",[572,1639,1641],{"className":1640,"ariaHidden":640},[639],[572,1642,1644,1647,1650],{"className":1643},[644],[572,1645],{"className":1646,"style":904},[648],[572,1648,607],{"className":1649},[653],[572,1651,973],{"className":1652},[653],[787,1654,1655],{},"Beim Ausklammern prüfen: Multipliziert man wieder aus, muss der Ausgangsterm herauskommen.",{"title":1657,"searchDepth":1658,"depth":1658,"links":1659},"",2,[1660,1661,1662],{"id":560,"depth":1658,"text":561},{"id":800,"depth":1658,"text":801},{"id":1391,"depth":1658,"text":1392},[1664,1667,1670,1673,1676,1679],{"lhs":1665,"rhs":1666},"a*(b+c)","a*b + a*c",{"lhs":1668,"rhs":1669},"3*(x+4)","3*x + 12",{"lhs":1671,"rhs":1672},"-2*(a-5)","-2*a + 10",{"lhs":1674,"rhs":1675},"6*x + 9","3*(2*x + 3)",{"lhs":1677,"rhs":1678},"7 * 102","7*100 + 7*2",{"lhs":1678,"rhs":1265},null,"md","distributive-law","a \\cdot (b + c) = a \\cdot b + a \\cdot c","\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>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a \\cdot (b + c) = a \\cdot b + a \\cdot c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7778em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","lower",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Falgebra\u002Fdistributivgesetz",[],[1691,1692],"expanding-brackets","binom-1",{"title":548,"description":1657},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fdistributivgesetz","Ein Faktor vor einer Klammer wird mit jedem Summanden in der Klammer multipliziert.",[1697,1698,1699,1700],"klammer","ausmultiplizieren","ausklammern","rechengesetz",[1702],{"symbol":1703,"meaning":1704,"symbolHtml":1705},"a, b, c","beliebige reelle Zahlen oder Terme","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b, c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","4wPp_W-EKvcgCy4u25T4M_FFIw2uHQh8QArnlQpVqfs",[1708,1711],{"stem":1709,"title":1710,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Ferste-binomische-formel","Erste binomische Formel",{"stem":1712,"title":1713,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fklammern-ausmultiplizieren","Zwei Klammern ausmultiplizieren",1793824271664]