因式分解 1331x^6y^9+216a^{12}b^{15}

解答

因式分解

1331 x^{6} y^{9} + 216 a^{12} b^{15}

(11 x^{2} y^{3} + 6 a^{4} b^{5}) (121 x^{4} y^{6} - 66 a^{4} b^{5} x^{2} y^{3} + 36 a^{8} b^{10})

求解步骤

1331 x^{6} y^{9} + 216 a^{12} b^{15}

将

1331 x^{6} y^{9}

改写为

(11 x^{2} y^{3})^{3}

将

216 a^{12} b^{15}

改写为

(6 a^{4} b^{5})^{3}

= (11 x^{2} y^{3})^{3} + (6 a^{4} b^{5})^{3}

使用立方和公式:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(11 x^{2} y^{3})^{3} + (6 a^{4} b^{5})^{3} = (11 x^{2} y^{3} + 6 a^{4} b^{5}) ((11 x^{2} y^{3})^{2} - 6 a^{4} b^{5} 11 x^{2} y^{3} + (6 a^{4} b^{5})^{2})

= (6 a^{4} b^{5} + 11 x^{2} y^{3}) ((6 a^{4} b^{5})^{2} - 6 a^{4} b^{5} 11 x^{2} y^{3} + (11 x^{2} y^{3})^{2})

化简

(11 x^{2} y^{3} + 6 a^{4} b^{5}) ((11 x^{2} y^{3})^{2} - 6 a^{4} b^{5} \cdot 11 x^{2} y^{3} + (6 a^{4} b^{5})^{2}) : (11 x^{2} y^{3} + 6 a^{4} b^{5}) (121 x^{4} y^{6} - 66 a^{4} b^{5} x^{2} y^{3} + 36 a^{8} b^{10})

= (11 x^{2} y^{3} + 6 a^{4} b^{5}) (121 x^{4} y^{6} - 66 a^{4} b^{5} x^{2} y^{3} + 36 a^{8} b^{10})

f a c t or \frac{1330 - 296 2}{105}

f a c t or 12 d e + 18 d^{2} e

f a c t or e^{j x} + e^{- j x}

f a c t or 2 + 23

f a c t or (x + 3) - (2 x^{2})