因数 (x-4)^3-(2x+5)^3

解

因数

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

(- x - 9) (7 x^{2} + 9 x + 21)

解答ステップ

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

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

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

改良

= (- x - 9) ((2 x + 5)^{2} + (x - 4) (2 x + 5) + (x - 4)^{2})

拡張

(x - 4)^{2} + (x - 4) (2 x + 5) + (2 x + 5)^{2} : 7 x^{2} + 9 x + 21

= (- x - 9) (7 x^{2} + 9 x + 21)