因数 (X+B)^3-X^3

解

因数

(X + B)^{3} - X^{3}

B (3 X^{2} + 3 XB + B^{2})

解答ステップ

(X + B)^{3} - X^{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 + B)^{3} - X^{3} = ((X + B) - X) ((X + B)^{2} + X (X + B) + X^{2})

= ((X + B) - X) (X^{2} + X (X + B) + (X + B)^{2})

改良

= B (X^{2} + X (X + B) + (X + B)^{2})

拡張

(X + B)^{2} + X (X + B) + X^{2} : 3 X^{2} + 3 XB + B^{2}

= B (3 X^{2} + 3 XB + B^{2})