因数 (x^2+xy^2)^2-(xy+y^2)^2

解

因数

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

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

解答ステップ

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

2乗の差の公式を適用する:

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

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

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

簡素化

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

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