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",[576,1187,1189,1203],{"className":1188},[579],[576,1190,1192],{"className":1191},[583],[585,1193,1194],{"xmlns":587},[589,1195,1196,1201],{},[592,1197,1198],{},[602,1199,1200],{},"0",[617,1202,1200],{"encoding":619},[576,1204,1206],{"className":1205,"ariaHidden":625},[624],[576,1207,1209,1213],{"className":1208},[629],[576,1210],{"className":1211,"style":1212},[633],"height:0.6444em;",[576,1214,1200],{"className":1215},[638],[559,1217,1219],{"id":1218},"beispiele","Beispiele",[576,1221,1223],{"className":1222},[737],[576,1224,1226,1273],{"className":1225},[579],[576,1227,1229],{"className":1228},[583],[585,1230,1231],{"xmlns":587,"display":746},[589,1232,1233,1270],{},[592,1234,1235,1237,1240,1242,1245,1247,1249,1251,1253,1255,1257,1259,1265,1267],{},[606,1236,754],{"stretchy":753},[598,1238,1239],{},"x",[606,1241,759],{},[602,1243,1244],{},"5",[606,1246,764],{"stretchy":753},[606,1248,754],{"stretchy":753},[598,1250,1239],{},[606,1252,608],{},[602,1254,1244],{},[606,1256,764],{"stretchy":753},[606,1258,777],{},[595,1260,1261,1263],{},[598,1262,1239],{},[602,1264,604],{},[606,1266,608],{},[602,1268,1269],{},"25",[617,1271,1272],{"encoding":619},"(x+5)(x-5) = x^2 - 25",[576,1274,1276,1297,1324,1345,1389],{"className":1275,"ariaHidden":625},[624],[576,1277,1279,1282,1285,1288,1291,1294],{"className":1278},[629],[576,1280],{"className":1281,"style":832},[633],[576,1283,754],{"className":1284},[836],[576,1286,1239],{"className":1287},[638,642],[576,1289],{"className":1290,"style":682},[681],[576,1292,759],{"className":1293},[686],[576,1295],{"className":1296,"style":682},[681],[576,1298,1300,1303,1306,1309,1312,1315,1318,1321],{"className":1299},[629],[576,1301],{"className":1302,"style":832},[633],[576,1304,1244],{"className":1305},[638],[576,1307,764],{"className":1308},[861],[576,1310,754],{"className":1311},[836],[576,1313,1239],{"className":1314},[638,642],[576,1316],{"className":1317,"style":682},[681],[576,1319,608],{"className":1320},[686],[576,1322],{"className":1323,"style":682},[681],[576,1325,1327,1330,1333,1336,1339,1342],{"className":1326},[629],[576,1328],{"className":1329,"style":832},[633],[576,1331,1244],{"className":1332},[638],[576,1334,764],{"className":1335},[861],[576,1337],{"className":1338,"style":892},[681],[576,1340,777],{"className":1341},[896],[576,1343],{"className":1344,"style":892},[681],[576,1346,1348,1351,1380,1383,1386],{"className":1347},[629],[576,1349],{"className":1350,"style":906},[633],[576,1352,1354,1357],{"className":1353},[638],[576,1355,1239],{"className":1356},[638,642],[576,1358,1360],{"className":1359},[646],[576,1361,1363],{"className":1362},[650],[576,1364,1366],{"className":1365},[654],[576,1367,1369],{"className":1368,"style":925},[658],[576,1370,1371,1374],{"style":928},[576,1372],{"className":1373,"style":667},[666],[576,1375,1377],{"className":1376},[671,672,673,674],[576,1378,604],{"className":1379},[638,674],[576,1381],{"className":1382,"style":682},[681],[576,1384,608],{"className":1385},[686],[576,1387],{"className":1388,"style":682},[681],[576,1390,1392,1395],{"className":1391},[629],[576,1393],{"className":1394,"style":1212},[633],[576,1396,1269],{"className":1397},[638],[576,1399,1401],{"className":1400},[737],[576,1402,1404,1458],{"className":1403},[579],[576,1405,1407],{"className":1406},[583],[585,1408,1409],{"xmlns":587,"display":746},[589,1410,1411,1455],{},[592,1412,1413,1415,1418,1421,1423,1425,1427,1429,1431,1433,1435,1437,1439,1441,1444,1450,1452],{},[606,1414,754],{"stretchy":753},[602,1416,1417],{},"3",[598,1419,1420],{},"y",[606,1422,759],{},[602,1424,604],{},[606,1426,764],{"stretchy":753},[606,1428,754],{"stretchy":753},[602,1430,1417],{},[598,1432,1420],{},[606,1434,608],{},[602,1436,604],{},[606,1438,764],{"stretchy":753},[606,1440,777],{},[602,1442,1443],{},"9",[595,1445,1446,1448],{},[598,1447,1420],{},[602,1449,604],{},[606,1451,608],{},[602,1453,1454],{},"4",[617,1456,1457],{"encoding":619},"(3y+2)(3y-2) = 9y^2 - 4",[576,1459,1461,1486,1516,1537,1585],{"className":1460,"ariaHidden":625},[624],[576,1462,1464,1467,1470,1473,1477,1480,1483],{"className":1463},[629],[576,1465],{"className":1466,"style":832},[633],[576,1468,754],{"className":1469},[836],[576,1471,1417],{"className":1472},[638],[576,1474,1420],{"className":1475,"style":1476},[638,642],"margin-right:0.0359em;",[576,1478],{"className":1479,"style":682},[681],[576,1481,759],{"className":1482},[686],[576,1484],{"className":1485,"style":682},[681],[576,1487,1489,1492,1495,1498,1501,1504,1507,1510,1513],{"className":1488},[629],[576,1490],{"className":1491,"style":832},[633],[576,1493,604],{"className":1494},[638],[576,1496,764],{"className":1497},[861],[576,1499,754],{"className":1500},[836],[576,1502,1417],{"className":1503},[638],[576,1505,1420],{"className":1506,"style":1476},[638,642],[576,1508],{"className":1509,"style":682},[681],[576,1511,608],{"className":1512},[686],[576,1514],{"className":1515,"style":682},[681],[576,1517,1519,1522,1525,1528,1531,1534],{"className":1518},[629],[576,1520],{"className":1521,"style":832},[633],[576,1523,604],{"className":1524},[638],[576,1526,764],{"className":1527},[861],[576,1529],{"className":1530,"style":892},[681],[576,1532,777],{"className":1533},[896],[576,1535],{"className":1536,"style":892},[681],[576,1538,1540,1544,1547,1576,1579,1582],{"className":1539},[629],[576,1541],{"className":1542,"style":1543},[633],"height:1.0585em;vertical-align:-0.1944em;",[576,1545,1443],{"className":1546},[638],[576,1548,1550,1553],{"className":1549},[638],[576,1551,1420],{"className":1552,"style":1476},[638,642],[576,1554,1556],{"className":1555},[646],[576,1557,1559],{"className":1558},[650],[576,1560,1562],{"className":1561},[654],[576,1563,1565],{"className":1564,"style":925},[658],[576,1566,1567,1570],{"style":928},[576,1568],{"className":1569,"style":667},[666],[576,1571,1573],{"className":1572},[671,672,673,674],[576,1574,604],{"className":1575},[638,674],[576,1577],{"className":1578,"style":682},[681],[576,1580,608],{"className":1581},[686],[576,1583],{"className":1584,"style":682},[681],[576,1586,1588,1591],{"className":1587},[629],[576,1589],{"className":1590,"style":1212},[633],[576,1592,1454],{"className":1593},[638],[564,1595,1596],{},"Kopfrechnen mit der Formel:",[576,1598,1600],{"className":1599},[737],[576,1601,1603,1662],{"className":1602},[579],[576,1604,1606],{"className":1605},[583],[585,1607,1608],{"xmlns":587,"display":746},[589,1609,1610,1659],{},[592,1611,1612,1615,1618,1621,1623,1625,1628,1630,1633,1635,1637,1639,1641,1643,1645,1647,1650,1652,1654,1656],{},[602,1613,1614],{},"21",[606,1616,1617],{},"⋅",[602,1619,1620],{},"19",[606,1622,777],{},[606,1624,754],{"stretchy":753},[602,1626,1627],{},"20",[606,1629,759],{},[602,1631,1632],{},"1",[606,1634,764],{"stretchy":753},[606,1636,754],{"stretchy":753},[602,1638,1627],{},[606,1640,608],{},[602,1642,1632],{},[606,1644,764],{"stretchy":753},[606,1646,777],{},[602,1648,1649],{},"400",[606,1651,608],{},[602,1653,1632],{},[606,1655,777],{},[602,1657,1658],{},"399",[617,1660,1661],{"encoding":619},"21 \\cdot 19 = (20+1)(20-1) = 400 - 1 = 399",[576,1663,1665,1683,1701,1722,1749,1770,1789,1807],{"className":1664,"ariaHidden":625},[624],[576,1666,1668,1671,1674,1677,1680],{"className":1667},[629],[576,1669],{"className":1670,"style":1212},[633],[576,1672,1614],{"className":1673},[638],[576,1675],{"className":1676,"style":682},[681],[576,1678,1617],{"className":1679},[686],[576,1681],{"className":1682,"style":682},[681],[576,1684,1686,1689,1692,1695,1698],{"className":1685},[629],[576,1687],{"className":1688,"style":1212},[633],[576,1690,1620],{"className":1691},[638],[576,1693],{"className":1694,"style":892},[681],[576,1696,777],{"className":1697},[896],[576,1699],{"className":1700,"style":892},[681],[576,1702,1704,1707,1710,1713,1716,1719],{"className":1703},[629],[576,1705],{"className":1706,"style":832},[633],[576,1708,754],{"className":1709},[836],[576,1711,1627],{"className":1712},[638],[576,1714],{"className":1715,"style":682},[681],[576,1717,759],{"className":1718},[686],[576,1720],{"className":1721,"style":682},[681],[576,1723,1725,1728,1731,1734,1737,1740,1743,1746],{"className":1724},[629],[576,1726],{"className":1727,"style":832},[633],[576,1729,1632],{"className":1730},[638],[576,1732,764],{"className":1733},[861],[576,1735,754],{"className":1736},[836],[576,1738,1627],{"className":1739},[638],[576,1741],{"className":1742,"style":682},[681],[576,1744,608],{"className":1745},[686],[576,1747],{"className":1748,"style":682},[681],[576,1750,1752,1755,1758,1761,1764,1767],{"className":1751},[629],[576,1753],{"className":1754,"style":832},[633],[576,1756,1632],{"className":1757},[638],[576,1759,764],{"className":1760},[861],[576,1762],{"className":1763,"style":892},[681],[576,1765,777],{"className":1766},[896],[576,1768],{"className":1769,"style":892},[681],[576,1771,1773,1777,1780,1783,1786],{"className":1772},[629],[576,1774],{"className":1775,"style":1776},[633],"height:0.7278em;vertical-align:-0.0833em;",[576,1778,1649],{"className":1779},[638],[576,1781],{"className":1782,"style":682},[681],[576,1784,608],{"className":1785},[686],[576,1787],{"className":1788,"style":682},[681],[576,1790,1792,1795,1798,1801,1804],{"className":1791},[629],[576,1793],{"className":1794,"style":1212},[633],[576,1796,1632],{"className":1797},[638],[576,1799],{"className":1800,"style":892},[681],[576,1802,777],{"className":1803},[896],[576,1805],{"className":1806,"style":892},[681],[576,1808,1810,1813],{"className":1809},[629],[576,1811],{"className":1812,"style":1212},[633],[576,1814,1658],{"className":1815},[638],[564,1817,1818],{},"Faktorisieren:",[576,1820,1822],{"className":1821},[737],[576,1823,1825,1871],{"className":1824},[579],[576,1826,1828],{"className":1827},[583],[585,1829,1830],{"xmlns":587,"display":746},[589,1831,1832,1868],{},[592,1833,1834,1840,1842,1845,1847,1849,1851,1853,1856,1858,1860,1862,1864,1866],{},[595,1835,1836,1838],{},[598,1837,1239],{},[602,1839,604],{},[606,1841,608],{},[602,1843,1844],{},"49",[606,1846,777],{},[606,1848,754],{"stretchy":753},[598,1850,1239],{},[606,1852,759],{},[602,1854,1855],{},"7",[606,1857,764],{"stretchy":753},[606,1859,754],{"stretchy":753},[598,1861,1239],{},[606,1863,608],{},[602,1865,1855],{},[606,1867,764],{"stretchy":753},[617,1869,1870],{"encoding":619},"x^2 - 49 = (x+7)(x-7)",[576,1872,1874,1918,1936,1957,1984],{"className":1873,"ariaHidden":625},[624],[576,1875,1877,1880,1909,1912,1915],{"className":1876},[629],[576,1878],{"className":1879,"style":906},[633],[576,1881,1883,1886],{"className":1882},[638],[576,1884,1239],{"className":1885},[638,642],[576,1887,1889],{"className":1888},[646],[576,1890,1892],{"className":1891},[650],[576,1893,1895],{"className":1894},[654],[576,1896,1898],{"className":1897,"style":925},[658],[576,1899,1900,1903],{"style":928},[576,1901],{"className":1902,"style":667},[666],[576,1904,1906],{"className":1905},[671,672,673,674],[576,1907,604],{"className":1908},[638,674],[576,1910],{"className":1911,"style":682},[681],[576,1913,608],{"className":1914},[686],[576,1916],{"className":1917,"style":682},[681],[576,1919,1921,1924,1927,1930,1933],{"className":1920},[629],[576,1922],{"className":1923,"style":1212},[633],[576,1925,1844],{"className":1926},[638],[576,1928],{"className":1929,"style":892},[681],[576,1931,777],{"className":1932},[896],[576,1934],{"className":1935,"style":892},[681],[576,1937,1939,1942,1945,1948,1951,1954],{"className":1938},[629],[576,1940],{"className":1941,"style":832},[633],[576,1943,754],{"className":1944},[836],[576,1946,1239],{"className":1947},[638,642],[576,1949],{"className":1950,"style":682},[681],[576,1952,759],{"className":1953},[686],[576,1955],{"className":1956,"style":682},[681],[576,1958,1960,1963,1966,1969,1972,1975,1978,1981],{"className":1959},[629],[576,1961],{"className":1962,"style":832},[633],[576,1964,1855],{"className":1965},[638],[576,1967,764],{"className":1968},[861],[576,1970,754],{"className":1971},[836],[576,1973,1239],{"className":1974},[638,642],[576,1976],{"className":1977,"style":682},[681],[576,1979,608],{"className":1980},[686],[576,1982],{"className":1983,"style":682},[681],[576,1985,1987,1990,1993],{"className":1986},[629],[576,1988],{"className":1989,"style":832},[633],[576,1991,1855],{"className":1992},[638],[576,1994,764],{"className":1995},[861],[559,1997,1999],{"id":1998},"typische-fehler","Typische Fehler",[2001,2002,2003,2350,2579],"ul",{},[2004,2005,2006,2116,2117,2209,2210,571],"li",{},[576,2007,2009,2034],{"className":2008},[579],[576,2010,2012],{"className":2011},[583],[585,2013,2014],{"xmlns":587},[589,2015,2016,2032],{},[592,2017,2018,2024,2026],{},[595,2019,2020,2022],{},[598,2021,600],{},[602,2023,604],{},[606,2025,608],{},[595,2027,2028,2030],{},[598,2029,613],{},[602,2031,604],{},[617,2033,620],{"encoding":619},[576,2035,2037,2081],{"className":2036,"ariaHidden":625},[624],[576,2038,2040,2043,2072,2075,2078],{"className":2039},[629],[576,2041],{"className":2042,"style":634},[633],[576,2044,2046,2049],{"className":2045},[638],[576,2047,600],{"className":2048},[638,642],[576,2050,2052],{"className":2051},[646],[576,2053,2055],{"className":2054},[650],[576,2056,2058],{"className":2057},[654],[576,2059,2061],{"className":2060,"style":659},[658],[576,2062,2063,2066],{"style":662},[576,2064],{"className":2065,"style":667},[666],[576,2067,2069],{"className":2068},[671,672,673,674],[576,2070,604],{"className":2071},[638,674],[576,2073],{"className":2074,"style":682},[681],[576,2076,608],{"className":2077},[686],[576,2079],{"className":2080,"style":682},[681],[576,2082,2084,2087],{"className":2083},[629],[576,2085],{"className":2086,"style":659},[633],[576,2088,2090,2093],{"className":2089},[638],[576,2091,613],{"className":2092},[638,642],[576,2094,2096],{"className":2095},[646],[576,2097,2099],{"className":2098},[650],[576,2100,2102],{"className":2101},[654],[576,2103,2105],{"className":2104,"style":659},[658],[576,2106,2107,2110],{"style":662},[576,2108],{"className":2109,"style":667},[666],[576,2111,2113],{"className":2112},[671,672,673,674],[576,2114,604],{"className":2115},[638,674]," mit ",[576,2118,2120,2146],{"className":2119},[579],[576,2121,2123],{"className":2122},[583],[585,2124,2125],{"xmlns":587},[589,2126,2127,2143],{},[592,2128,2129,2131,2133,2135,2137],{},[606,2130,754],{"stretchy":753},[598,2132,600],{},[606,2134,608],{},[598,2136,613],{},[595,2138,2139,2141],{},[606,2140,764],{"stretchy":753},[602,2142,604],{},[617,2144,2145],{"encoding":619},"(a-b)^2",[576,2147,2149,2170],{"className":2148,"ariaHidden":625},[624],[576,2150,2152,2155,2158,2161,2164,2167],{"className":2151},[629],[576,2153],{"className":2154,"style":832},[633],[576,2156,754],{"className":2157},[836],[576,2159,600],{"className":2160},[638,642],[576,2162],{"className":2163,"style":682},[681],[576,2165,608],{"className":2166},[686],[576,2168],{"className":2169,"style":682},[681],[576,2171,2173,2177,2180],{"className":2172},[629],[576,2174],{"className":2175,"style":2176},[633],"height:1.0641em;vertical-align:-0.25em;",[576,2178,613],{"className":2179},[638,642],[576,2181,2183,2186],{"className":2182},[861],[576,2184,764],{"className":2185},[861],[576,2187,2189],{"className":2188},[646],[576,2190,2192],{"className":2191},[650],[576,2193,2195],{"className":2194},[654],[576,2196,2198],{"className":2197,"style":659},[658],[576,2199,2200,2203],{"style":662},[576,2201],{"className":2202,"style":667},[666],[576,2204,2206],{"className":2205},[671,672,673,674],[576,2207,604],{"className":2208},[638,674]," verwechseln. Das ist die zweite binomische Formel und ergibt ",[576,2211,2213,2247],{"className":2212},[579],[576,2214,2216],{"className":2215},[583],[585,2217,2218],{"xmlns":587},[589,2219,2220,2244],{},[592,2221,2222,2228,2230,2232,2234,2236,2238],{},[595,2223,2224,2226],{},[598,2225,600],{},[602,2227,604],{},[606,2229,608],{},[602,2231,604],{},[598,2233,600],{},[598,2235,613],{},[606,2237,759],{},[595,2239,2240,2242],{},[598,2241,613],{},[602,2243,604],{},[617,2245,2246],{"encoding":619},"a^2 - 2ab + b^2",[576,2248,2250,2294,2315],{"className":2249,"ariaHidden":625},[624],[576,2251,2253,2256,2285,2288,2291],{"className":2252},[629],[576,2254],{"className":2255,"style":634},[633],[576,2257,2259,2262],{"className":2258},[638],[576,2260,600],{"className":2261},[638,642],[576,2263,2265],{"className":2264},[646],[576,2266,2268],{"className":2267},[650],[576,2269,2271],{"className":2270},[654],[576,2272,2274],{"className":2273,"style":659},[658],[576,2275,2276,2279],{"style":662},[576,2277],{"className":2278,"style":667},[666],[576,2280,2282],{"className":2281},[671,672,673,674],[576,2283,604],{"className":2284},[638,674],[576,2286],{"className":2287,"style":682},[681],[576,2289,608],{"className":2290},[686],[576,2292],{"className":2293,"style":682},[681],[576,2295,2297,2300,2303,2306,2309,2312],{"className":2296},[629],[576,2298],{"className":2299,"style":953},[633],[576,2301,604],{"className":2302},[638],[576,2304,957],{"className":2305},[638,642],[576,2307],{"className":2308,"style":682},[681],[576,2310,759],{"className":2311},[686],[576,2313],{"className":2314,"style":682},[681],[576,2316,2318,2321],{"className":2317},[629],[576,2319],{"className":2320,"style":659},[633],[576,2322,2324,2327],{"className":2323},[638],[576,2325,613],{"className":2326},[638,642],[576,2328,2330],{"className":2329},[646],[576,2331,2333],{"className":2332},[650],[576,2334,2336],{"className":2335},[654],[576,2337,2339],{"className":2338,"style":659},[658],[576,2340,2341,2344],{"style":662},[576,2342],{"className":2343,"style":667},[666],[576,2345,2347],{"className":2346},[671,672,673,674],[576,2348,604],{"className":2349},[638,674],[2004,2351,2352,2463,2464,2574,2575,2578],{},[576,2353,2355,2381],{"className":2354},[579],[576,2356,2358],{"className":2357},[583],[585,2359,2360],{"xmlns":587},[589,2361,2362,2378],{},[592,2363,2364,2370,2372],{},[595,2365,2366,2368],{},[598,2367,600],{},[602,2369,604],{},[606,2371,759],{},[595,2373,2374,2376],{},[598,2375,613],{},[602,2377,604],{},[617,2379,2380],{"encoding":619},"a^2 + b^2",[576,2382,2384,2428],{"className":2383,"ariaHidden":625},[624],[576,2385,2387,2390,2419,2422,2425],{"className":2386},[629],[576,2388],{"className":2389,"style":634},[633],[576,2391,2393,2396],{"className":2392},[638],[576,2394,600],{"className":2395},[638,642],[576,2397,2399],{"className":2398},[646],[576,2400,2402],{"className":2401},[650],[576,2403,2405],{"className":2404},[654],[576,2406,2408],{"className":2407,"style":659},[658],[576,2409,2410,2413],{"style":662},[576,2411],{"className":2412,"style":667},[666],[576,2414,2416],{"className":2415},[671,672,673,674],[576,2417,604],{"className":2418},[638,674],[576,2420],{"className":2421,"style":682},[681],[576,2423,759],{"className":2424},[686],[576,2426],{"className":2427,"style":682},[681],[576,2429,2431,2434],{"className":2430},[629],[576,2432],{"className":2433,"style":659},[633],[576,2435,2437,2440],{"className":2436},[638],[576,2438,613],{"className":2439},[638,642],[576,2441,2443],{"className":2442},[646],[576,2444,2446],{"className":2445},[650],[576,2447,2449],{"className":2448},[654],[576,2450,2452],{"className":2451,"style":659},[658],[576,2453,2454,2457],{"style":662},[576,2455],{"className":2456,"style":667},[666],[576,2458,2460],{"className":2459},[671,672,673,674],[576,2461,604],{"className":2462},[638,674]," wie 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zerlegen. Eine ",[568,2576,2577],{},"Summe"," von Quadraten lässt sich mit reellen Zahlen nicht in dieser Form faktorisieren.",[2004,2580,2581,2582,2714,2715,571],{},"Bei Faktoren den ganzen Summanden quadrieren: ",[576,2583,2585,2619],{"className":2584},[579],[576,2586,2588],{"className":2587},[583],[585,2589,2590],{"xmlns":587},[589,2591,2592,2616],{},[592,2593,2594,2596,2598,2600,2606,2608,2610],{},[606,2595,754],{"stretchy":753},[602,2597,1417],{},[598,2599,1420],{},[595,2601,2602,2604],{},[606,2603,764],{"stretchy":753},[602,2605,604],{},[606,2607,777],{},[602,2609,1443],{},[595,2611,2612,2614],{},[598,2613,1420],{},[602,2615,604],{},[617,2617,2618],{"encoding":619},"(3y)^2 = 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nicht 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