因式分解 (a+b)^3-b^3

解答

因式分解

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

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

求解步骤

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

使用立方差公式:

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

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

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

整理后得

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

乘开

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

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

f a c t or \frac{1}{3} x^{2} - 3 x + 5

f a c t or e (- 2)

f a c t or - (\frac{7}{8})

f a c t or (2 x - 5)^{2} + 6 (2 x - 5) + 5

f a c t or sin (4 x - 8 y)