因数 (x+y)^4-1

解

因数

(x + y)^{4} - 1

(x^{2} + 2 x y + y^{2} + 1) (x + y + 1) (x + y - 1)

解答ステップ

(x + y)^{4} - 1

(x + y)^{4} = ((x + y)^{2})^{2}

1 = 1^{2}

= ((x + y)^{2})^{2} - 1^{2}

2乗の差の公式を適用する:

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

((x + y)^{2})^{2} - 1^{2} = ((x + y)^{2} + 1) ((x + y)^{2} - 1)

= ((x + y)^{2} + 1) ((x + y)^{2} - 1)

因数

(x + y)^{2} - 1 : (x + y + 1) (x + y - 1)

= ((x + y)^{2} + 1) (x + y + 1) (x + y - 1)

拡張

(x + y)^{2} + 1 : x^{2} + 2 x y + y^{2} + 1

= (x^{2} + 2 x y + y^{2} + 1) (x + y + 1) (x + y - 1)