因数 (x+y)^3-(x-y)^3

解

因数

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

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

解答ステップ

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

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

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

改良

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

拡張

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

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