因式分解 64b^3+125a^3

解答

因式分解

64 b^{3} + 125 a^{3}

(4 b + 5 a) (16 b^{2} - 20 ba + 25 a^{2})

求解步骤

64 b^{3} + 125 a^{3}

使用指数运算法则

= (4 b)^{3} + (5 a)^{3}

使用立方和公式:

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

(4 b)^{3} + (5 a)^{3} = (4 b + 5 a) ((4 b)^{2} - 4 b \cdot 5 a + (5 a)^{2})

= (4 b + 5 a) ((4 b)^{2} - 4 b \cdot 5 a + (5 a)^{2})

化简

(4 b)^{2} - 4 b \cdot 5 a + (5 a)^{2} : 16 b^{2} - 20 ba + 25 a^{2}

= (4 b + 5 a) (16 b^{2} - 20 ba + 25 a^{2})

s im pl i f y lo g_{10} (1100)

e x p an d (3 z - 2)^{3}

f a c t or 20 n^{2} - 9 n - 20

j o in \frac{π}{2} + 4 π

s im pl i f y (- 2) + (- 3)