因式分解 32x^5-1

解答

因式分解

32 x^{5} - 1

(2 x - 1) (16 x^{4} + 8 x^{3} + 4 x^{2} + 2 x + 1)

求解步骤

32 x^{5} - 1

使用指数运算法则

= (2 x)^{5} - 1^{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})

(2 x)^{5} - 1^{5} = (2 x - 1) (2^{4} x^{4} + 2^{3} x^{3} + 2^{2} x^{2} + 2 x + 1)

= (2 x - 1) (2^{4} x^{4} + 2^{3} x^{3} + 2^{2} x^{2} + 2 x + 1)

化简

(2 x - 1) (2^{4} x^{4} + 2^{3} x^{3} + 2^{2} x^{2} + 2 x + 1) : (2 x - 1) (16 x^{4} + 8 x^{3} + 4 x^{2} + 2 x + 1)

= (2 x - 1) (16 x^{4} + 8 x^{3} + 4 x^{2} + 2 x + 1)

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

f a c t or 6 x^{2} + 17 x y + 5 y^{2}

s im pl i f y (x) - 3 x + x^{2} - x^{4}

s im pl i f y \frac{( x ^{2} )}{( y ^{3} ) \cdot ( \frac{x}{y} ) ^{- 2} \cdot y ^{- 1}}

s im pl i f y \frac{1}{( \frac{a}{2} ) ^{2}} - \frac{1}{a ^{2}}