因式分解 125x^3-8y^3

解答

因式分解

125 x^{3} - 8 y^{3}

(5 x - 2 y) (25 x^{2} + 10 x y + 4 y^{2})

求解步骤

125 x^{3} - 8 y^{3}

使用指数运算法则

= (5 x)^{3} - (2 y)^{3}

使用立方差公式:

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

(5 x)^{3} - (2 y)^{3} = (5 x - 2 y) ((5 x)^{2} + 5 x \cdot 2 y + (2 y)^{2})

= (5 x - 2 y) ((5 x)^{2} + 5 x \cdot 2 y + (2 y)^{2})

化简

(5 x)^{2} + 5 x \cdot 2 y + (2 y)^{2} : 25 x^{2} + 10 x y + 4 y^{2}

= (5 x - 2 y) (25 x^{2} + 10 x y + 4 y^{2})

4 x^{2} - 1 = 0

(x - 2)^{2} + 48 = (2 - 3 x)^{2}

s im pl i f y (14 - 3) (12 + 7)

- x^{2} + 2 x + 2 = 0

16 x^{2} - 3 = 8 x