因数 (5x+1)^3+8

解

因数

(5 x + 1)^{3} + 8

(5 x + 3) (25 x^{2} + 3)

解答ステップ

(5 x + 1)^{3} + 8

8

を書き換え

2^{3}

= (5 x + 1)^{3} + 2^{3}

立方数の和の公式を適用する:

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

(5 x + 1)^{3} + 2^{3} = ((5 x + 1) + 2) ((5 x + 1)^{2} - 2 (5 x + 1) + 2^{2})

= ((5 x + 1) + 2) ((5 x + 1)^{2} - 2 (5 x + 1) + 2^{2})

改良

= (5 x + 3) ((5 x + 1)^{2} - 2 (5 x + 1) + 4)

拡張

(5 x + 1)^{2} - 2 (5 x + 1) + 4 : 25 x^{2} + 3

= (5 x + 3) (25 x^{2} + 3)