因数 (a+b)^3-(a-b)^3

解

因数

(a + b)^{3} - (a - b)^{3}

2 b (3 a^{2} + b^{2})

解答ステップ

(a + b)^{3} - (a - b)^{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})

(a + b)^{3} - (a - b)^{3} = ((a + b) - (a - b)) ((a + b)^{2} + (a - b) (a + b) + (a - b)^{2})

= ((a + b) - (a - b)) ((a - b)^{2} + (a - b) (a + b) + (a + b)^{2})

改良

= 2 b ((a + b)^{2} + (a - b) (a + b) + (a - b)^{2})

拡張

(a + b)^{2} + (a - b) (a + b) + (a - b)^{2} : 3 a^{2} + b^{2}

= 2 b (3 a^{2} + b^{2})