因数 (x+y)^3+(x-y)^3

解

因数

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

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

解答ステップ

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

立方数の和の公式を適用する:

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

拡張

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

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