因数 1-4x^2+12xy-9y^2

解

因数

1 - 4 x^{2} + 12 x y - 9 y^{2}

(1 + 2 x - 3 y) (1 - 2 x + 3 y)

解答ステップ

1 - 4 x^{2} + 12 x y - 9 y^{2}

因数

- 4 x^{2} + 12 x y - 9 y^{2} : - (2 x - 3 y)^{2}

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

1

を書き換え

1^{2}

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

2乗の差の公式を適用する:

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

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

= (1 + (2 x - 3 y)) (1 - (2 x - 3 y))

簡素化

(1 + (2 x - 3 y)) (1 - (2 x - 3 y)) : (1 + 2 x - 3 y) (1 - 2 x + 3 y)

= (1 + 2 x - 3 y) (1 - 2 x + 3 y)