What is factor x^9-512 ?

The solution to factor x^9-512 is (x-2)(x^2+2x+4)(x^6+8x^3+64)

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factor x^9-512

factor

x^{9} - 512

(x - 2) (x^{2} + 2 x + 4) (x^{6} + 8 x^{3} + 64)

Solution steps

x^{9} - 512

Apply exponent rules

= (x^{3})^{3} - 8^{3}

Apply Difference of Cubes Formula:

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

(x^{3})^{3} - 8^{3} = (x^{3} - 8) (x^{6} + 8 x^{3} + 8^{2})

= (x^{3} - 8) (x^{6} + 8 x^{3} + 8^{2})

Factor

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

= (x - 2) (x^{2} + 2 x + 2^{2}) (x^{6} + 8 x^{3} + 8^{2})

Simplify

(x - 2) (x^{2} + 2 x + 2^{2}) (x^{6} + 8 x^{3} + 8^{2}) : (x - 2) (x^{2} + 2 x + 4) (x^{6} + 8 x^{3} + 64)

= (x - 2) (x^{2} + 2 x + 4) (x^{6} + 8 x^{3} + 64)

\frac{x}{x + 4} - \frac{6}{x - 1}

\frac{2}{3} y - 2 (\frac{4}{3} y + z)

- 4 i \cdot i

\frac{- 1}{2} \div \frac{5}{4}

3 \cdot 4 x

What is factor x^9-512 ?
The solution to factor x^9-512 is (x-2)(x^2+2x+4)(x^6+8x^3+64)