因数 49x^4-4(x^2-3x)^2

解

因数

49 x^{4} - 4 (x^{2} - 3 x)^{2}

3 x^{2} (3 x - 2) (5 x + 6)

解答ステップ

49 x^{4} - 4 (x^{2} - 3 x)^{2}

49 x^{4} = (7 x^{2})^{2}

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

= (7 x^{2})^{2} - (2 (x^{2} - 3 x))^{2}

2乗の差の公式を適用する:

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

(7 x^{2})^{2} - (2 (x^{2} - 3 x))^{2} = (7 x^{2} + 2 (x^{2} - 3 x)) (7 x^{2} - 2 (x^{2} - 3 x))

= (7 x^{2} + 2 (x^{2} - 3 x)) (7 x^{2} - 2 (x^{2} - 3 x))

因数

7 x^{2} + 2 (x^{2} - 3 x) : 3 x (3 x - 2)

因数

7 x^{2} - 2 (x^{2} - 3 x) : x (5 x + 6)

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

指数の規則を適用する:

aa = a^{2}

xx = x^{2}

= 3 x^{2} (3 x - 2) (5 x + 6)