因数 x^2+12x+36-9y^2

解

因数

x^{2} + 12 x + 36 - 9 y^{2}

(x + 6 + 3 y) (x + 6 - 3 y)

解答ステップ

x^{2} + 12 x + 36 - 9 y^{2}

因数

x^{2} + 12 x + 36 : (x + 6)^{2}

= (x + 6)^{2} - 9 y^{2}

簡素化

9 y^{2} : (3 y)^{2}

= (x + 6)^{2} - (3 y)^{2}

2乗の差の公式を適用する:

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

(x + 6)^{2} - (3 y)^{2} = ((x + 6) + 3 y) ((x + 6) - 3 y)

= ((x + 6) + 3 y) ((x + 6) - 3 y)

規則を適用する:

(a) = a

(x + 6) = x + 6

= (x + 6 + 3 y) (x + 6 - 3 y)