因式分解 x^8+4x^4y^4+16y^8

解答

因式分解

x^{8} + 4 x^{4} y^{4} + 16 y^{8}

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

求解步骤

x^{8} + 4 x^{4} y^{4} + 16 y^{8}

加和减

4 x^{4} y^{4}

= x^{8} + 8 x^{4} y^{4} + 16 y^{8} - 4 x^{4} y^{4}

因式分解

x^{8} + 8 x^{4} y^{4} + 16 y^{8} : (x^{4} + 4 y^{4})^{2}

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

使用指数运算法则

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

因式分解

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

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

s im pl i f y \frac{( 3 s ^{- 3} ) ^{5}}{3 s ^{- 2}}

f a c t or 64 - m^{6}

s im pl i f y \frac{7}{13} \times \frac{2}{3}

s im pl i f y (1 + 0.0001)^{\frac{1}{0.0001}}

e x p an d (2 x^{2} + 5 y^{4})^{3}