因数 1-9x^2+24xy-16y^2

解

因数

1 - 9 x^{2} + 24 x y - 16 y^{2}

(1 + 3 x - 4 y) (1 - 3 x + 4 y)

解答ステップ

1 - 9 x^{2} + 24 x y - 16 y^{2}

因数

- 9 x^{2} + 24 x y - 16 y^{2} : - (3 x - 4 y)^{2}

= 1 - (3 x - 4 y)^{2}

1

を書き換え

1^{2}

= 1^{2} - (3 x - 4 y)^{2}

2乗の差の公式を適用する:

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

1^{2} - (3 x - 4 y)^{2} = (1 + (3 x - 4 y)) (1 - (3 x - 4 y))

= (1 + (3 x - 4 y)) (1 - (3 x - 4 y))

簡素化

(1 + (3 x - 4 y)) (1 - (3 x - 4 y)) : (1 + 3 x - 4 y) (1 - 3 x + 4 y)

= (1 + 3 x - 4 y) (1 - 3 x + 4 y)