因数 (3x+1)^2-(x-4)^2

解

因数

(3 x + 1)^{2} - (x - 4)^{2}

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

解答ステップ

(3 x + 1)^{2} - (x - 4)^{2}

2乗の差の公式を適用する:

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

(3 x + 1)^{2} - (x - 4)^{2} = ((3 x + 1) + (x - 4)) ((3 x + 1) - (x - 4))

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

簡素化

((3 x + 1) + (x - 4)) ((3 x + 1) - (x - 4)) : (4 x - 3) (2 x + 5)

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