因数 (2x+1)^3-8

解

因数

(2 x + 1)^{3} - 8

(2 x - 1) (4 x^{2} + 8 x + 7)

解答ステップ

(2 x + 1)^{3} - 8

8

を書き換え

2^{3}

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

立方数の差の公式を適用する:

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

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

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

改良

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

拡張

(2 x + 1)^{2} + 2 (2 x + 1) + 4 : 4 x^{2} + 8 x + 7

= (2 x - 1) (4 x^{2} + 8 x + 7)