因数 x^3-x^2-x*y^2+y^2

解

因数

x^{3} - x^{2} - x \cdot y^{2} + y^{2}

(x - 1) (x + y) (x - y)

解答ステップ

x^{3} - x^{2} - x y^{2} + y^{2}

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

x^{2}

を

x^{3} - x^{2} : x^{2} (x - 1)

からくくり出す

y^{2}

を

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

からくくり出す

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

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

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

共通項をくくり出す

x - 1

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

因数

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

= (x - 1) (x + y) (x - y)