因式分解 32x^5-y^5

解答

因式分解

32 x^{5} - y^{5}

(2 x - y) (16 x^{4} + 8 x^{3} y + 4 x^{2} y^{2} + 2 x y^{3} + y^{4})

求解步骤

32 x^{5} - y^{5}

使用指数运算法则

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

使用因式分解法则:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1}), n i s o dd

(2 x)^{5} - y^{5} = (2 x - y) (2^{4} x^{4} + 2^{3} x^{3} y + 2^{2} x^{2} y^{2} + 2 x y^{3} + y^{4})

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

化简

(2 x - y) (2^{4} x^{4} + 2^{3} x^{3} y + 2^{2} x^{2} y^{2} + 2 x y^{3} + y^{4}) : (2 x - y) (16 x^{4} + 8 x^{3} y + 4 x^{2} y^{2} + 2 x y^{3} + y^{4})

= (2 x - y) (16 x^{4} + 8 x^{3} y + 4 x^{2} y^{2} + 2 x y^{3} + y^{4})

f a c t or m^{6} + 9 m^{4} + 24 m^{2} + 16

s im pl i f y 2021 \cdot 2022 - 500 \cdot 4044 - 21 \cdot 2022

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

s im pl i f y (- 2 x^{5})^{5} \cdot (- 5 x^{2})^{2}

f a c t or x^{4} + 5 x^{3} - 5 x^{2} + 5 x - 6