What is factor 32x^5-1 ?

The solution to factor 32x^5-1 is (2x-1)(16x^4+8x^3+4x^2+2x+1)

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factor 32x^5-1

factor

32 x^{5} - 1

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

Solution steps

32 x^{5} - 1

Apply exponent rules

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

Apply factoring rule:

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)

Simplify

(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)

2 (x + 3)^{3}

6 x^{2} + 17 x y + 5 y^{2}

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

\frac{( x ^{2} )}{( y ^{3} ) \cdot ( \frac{x}{y} ) ^{- 2} \cdot y ^{- 1}}

\frac{1}{( \frac{a}{2} ) ^{2}} - \frac{1}{a ^{2}}

What is factor 32x^5-1 ?
The solution to factor 32x^5-1 is (2x-1)(16x^4+8x^3+4x^2+2x+1)