因数 (2x+1)^2-(x-3)^2

解

因数

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

(3 x - 2) (x + 4)

解答ステップ

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

2乗の差の公式を適用する:

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

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

= ((2 x + 1) + (x - 3)) ((2 x + 1) - (x - 3))

簡素化

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

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