因式分解 8m^3-125n^3

解答

因式分解

8 m^{3} - 125 n^{3}

(2 m - 5 n) (4 m^{2} + 10 mn + 25 n^{2})

求解步骤

8 m^{3} - 125 n^{3}

使用指数运算法则

= (2 m)^{3} - (5 n)^{3}

使用立方差公式:

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

(2 m)^{3} - (5 n)^{3} = (2 m - 5 n) ((2 m)^{2} + 2 m \cdot 5 n + (5 n)^{2})

= (2 m - 5 n) ((2 m)^{2} + 2 m \cdot 5 n + (5 n)^{2})

化简

(2 m)^{2} + 2 m \cdot 5 n + (5 n)^{2} : 4 m^{2} + 10 mn + 25 n^{2}

= (2 m - 5 n) (4 m^{2} + 10 mn + 25 n^{2})

f a c t or 5 x + 10 y

f a c t or 4 z^{2} - 4 z + 1

s im pl i f y [(x^{2} - 5) (x^{2} + 5)]^{2} x^{0}

s im pl i f y (lo g_{10} (a^{b}))^{2}

s im pl i f y f - 0.5 f