因数 (3x-2y)^3-(5y+3x)^3

解

因数

(3 x - 2 y)^{3} - (5 y + 3 x)^{3}

- 7 y (27 x^{2} + 27 x y + 19 y^{2})

解答ステップ

(3 x - 2 y)^{3} - (5 y + 3 x)^{3}

立方数の差の公式を適用する:

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

(3 x - 2 y)^{3} - (5 y + 3 x)^{3} = ((3 x - 2 y) - (5 y + 3 x)) ((3 x - 2 y)^{2} + (5 y + 3 x) (3 x - 2 y) + (5 y + 3 x)^{2})

= ((3 x - 2 y) - (5 y + 3 x)) ((5 y + 3 x)^{2} + (5 y + 3 x) (3 x - 2 y) + (3 x - 2 y)^{2})

改良

= - 7 y ((3 x + 5 y) (3 x - 2 y) + (3 x + 5 y)^{2} + (3 x - 2 y)^{2})

拡張

(3 x - 2 y)^{2} + (5 y + 3 x) (3 x - 2 y) + (5 y + 3 x)^{2} : 27 x^{2} + 27 x y + 19 y^{2}

= - 7 y (27 x^{2} + 27 x y + 19 y^{2})