因式分解 a^3+8b^6

解答

因式分解

a^{3} + 8 b^{6}

(a + 2 b^{2}) (a^{2} - 2 a b^{2} + 4 b^{4})

求解步骤

a^{3} + 8 b^{6}

使用指数运算法则

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

使用立方和公式:

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

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

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

化简

a^{2} - a \cdot 2 b^{2} + (2 b^{2})^{2} : a^{2} - 2 a b^{2} + 4 b^{4}

= (a + 2 b^{2}) (a^{2} - 2 a b^{2} + 4 b^{4})

s im pl i f y \frac{sin ( 2 y )}{cos ^{2} ( y )}

s im pl i f y (6 x + 3) 3

s im pl i f y 3 x + 8 x - 6 x - 9

e x p an d (- 4 + 5 j) (- 3 - 2 j)

f a c t or (1 + x^{2} + x^{3} + x)^{6}