因式分解 125x^3-1

解答

因式分解

125 x^{3} - 1

(5 x - 1) (25 x^{2} + 5 x + 1)

求解步骤

125 x^{3} - 1

使用指数运算法则

= (5 x)^{3} - 1^{3}

使用立方差公式:

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

(5 x)^{3} - 1^{3} = (5 x - 1) (5^{2} x^{2} + 5 x + 1)

= (5 x - 1) (5^{2} x^{2} + 5 x + 1)

5^{2} = 25

= (5 x - 1) (25 x^{2} + 5 x + 1)

- 4 x + 15 \leq 35

s im pl i f y \frac{2 - 1}{1 + i}

(x + 4)^{3} - (x - 3)^{3} = 343

f a c t or u^{2} + 8 u + 7

3 (x + 1) + 11 < - 2 (x + 13)