因数 (x^2+8)^2-36x^2

解

因数

(x^{2} + 8)^{2} - 36 x^{2}

(x + 2) (x + 4) (x - 2) (x - 4)

解答ステップ

(x^{2} + 8)^{2} - 36 x^{2}

簡素化

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

= (x^{2} + 8)^{2} - (6 x)^{2}

2乗の差の公式を適用する:

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

(x^{2} + 8)^{2} - (6 x)^{2} = ((x^{2} + 8) + 6 x) ((x^{2} + 8) - 6 x)

= ((x^{2} + 8) + 6 x) ((x^{2} + 8) - 6 x)

規則を適用する:

(a) = a

(x^{2} + 8) = x^{2} + 8

= (x^{2} + 8 + 6 x) (x^{2} + 8 - 6 x)

= (x^{2} + 6 x + 8) (x^{2} - 6 x + 8)

因数

x^{2} + 6 x + 8 : (x + 2) (x + 4)

因数

x^{2} - 6 x + 8 : (x - 2) (x - 4)

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