因数 x^2-1+2a-a^2

解

因数

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

(x + a - 1) (x - a + 1)

解答ステップ

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

因数

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

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

2乗の差の公式を適用する:

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

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

= (x + (a - 1)) (x - (a - 1))

簡素化

(x + (a - 1)) (x - (a - 1)) : (x + a - 1) (x - a + 1)

= (x + a - 1) (x - a + 1)