因数 (5x+2)^2-(3x-4)^2

解

因数

(5 x + 2)^{2} - (3 x - 4)^{2}

4 (4 x - 1) (x + 3)

解答ステップ

(5 x + 2)^{2} - (3 x - 4)^{2}

2乗の差の公式を適用する:

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

(5 x + 2)^{2} - (3 x - 4)^{2} = ((5 x + 2) + (3 x - 4)) ((5 x + 2) - (3 x - 4))

= ((5 x + 2) + (3 x - 4)) ((5 x + 2) - (3 x - 4))

簡素化

((5 x + 2) + (3 x - 4)) ((5 x + 2) - (3 x - 4)) : (8 x - 2) (2 x + 6)

= (8 x - 2) (2 x + 6)

因数

8 x - 2 : 2 (4 x - 1)

因数

2 x + 6 : 2 (x + 3)

= 2 (4 x - 1) \cdot 2 (x + 3)

数を乗じる:

2 \cdot 2 = 4

= 4 (4 x - 1) (x + 3)