因数-(x+2y)^2+16(x+y)^2

解

因数

- (x + 2 y)^{2} + 16 (x + y)^{2}

(5 x + 6 y) (3 x + 2 y)

解答ステップ

- (x + 2 y)^{2} + 16 (x + y)^{2}

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

を書き換え

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

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

2乗の差の公式を適用する:

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

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

= (4 (x + y) + (x + 2 y)) (4 (x + y) - (x + 2 y))

改良

= (x + 2 y + 4 (x + y)) (4 (x + y) - x - 2 y)

拡張

4 (x + y) + x + 2 y : 5 x + 6 y

= (5 x + 6 y) (4 (x + y) - x - 2 y)

拡張

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

= (5 x + 6 y) (3 x + 2 y)