因式分解 x^3-125a^6

解答

因式分解

x^{3} - 125 a^{6}

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

求解步骤

x^{3} - 125 a^{6}

使用指数运算法则

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

使用立方差公式:

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

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

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

化简

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

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

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

s im pl i f y (x + 2)^{2} + (y - 1)^{2}

s im pl i f y \frac{2}{5} + \frac{5}{7}

s im pl i f y \frac{3 ( h ^{- 5} ) ^{4}}{6 h ^{6}}

s im pl i f y 5 x - 3 x^{2} + 16 x^{2}

s im pl i f y 21 - 5 + 7