因数 x^2y^2-x^2-1+y^2

解

因数

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

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

解答ステップ

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

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

x^{2}

を

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

からくくり出す

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

共通項をくくり出す

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

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

因数

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

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