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受欢迎的代数 >

因式分解 x^6-8y^{12}

解答

因式分解

x^{6} - 8 y^{12}

解答

(x^{2} - 2 y^{4}) (x^{4} + 2 x^{2} y^{4} + 4 y^{8})

求解步骤

x^{6} - 8 y^{12}

使用指数运算法则

= (x^{2})^{3} - (2 y^{4})^{3}

使用立方差公式:

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

(x^{2})^{3} - (2 y^{4})^{3} = (x^{2} - 2 y^{4}) ((x^{2})^{2} + x^{2} \cdot 2 y^{4} + (2 y^{4})^{2})

= (x^{2} - 2 y^{4}) ((x^{2})^{2} + x^{2} \cdot 2 y^{4} + (2 y^{4})^{2})

化简

(x^{2})^{2} + x^{2} \cdot 2 y^{4} + (2 y^{4})^{2} : x^{4} + 2 x^{2} y^{4} + 4 y^{8}

= (x^{2} - 2 y^{4}) (x^{4} + 2 x^{2} y^{4} + 4 y^{8})

流行的例子

∣ x - 1 ∣ - ∣ x - 2 ∣ = 0

\frac{7}{6} x - 5 = 4

2 x - 3 > x + 5

5 x + 2 = 7 x - 4

化简 (7sqrt(90))/(2sqrt(70))

s im pl i f y \frac{7 90}{2 70}