What is factor 512x^6-27y^3z^9 ?

The solution to factor 512x^6-27y^3z^9 is (8x^2-3yz^3)(64x^4+24x^2yz^3+9y^2z^6)

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factor 512x^6-27y^3z^9

factor

512 x^{6} - 27 y^{3} z^{9}

(8 x^{2} - 3 y z^{3}) (64 x^{4} + 24 x^{2} y z^{3} + 9 y^{2} z^{6})

Solution steps

512 x^{6} - 27 y^{3} z^{9}

Rewrite

512 x^{6}

(2^{3} x^{2})^{3}

Rewrite

27 y^{3} z^{9}

(3 y z^{3})^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(2^{3} x^{2} - 3 y z^{3}) ((2^{3} x^{2})^{2} + 2^{3} x^{2} \cdot 3 y z^{3} + (3 y z^{3})^{2}) : (8 x^{2} - 3 y z^{3}) (64 x^{4} + 24 x^{2} y z^{3} + 9 y^{2} z^{6})

= (8 x^{2} - 3 y z^{3}) (64 x^{4} + 24 x^{2} y z^{3} + 9 y^{2} z^{6})

3 x^{2} + 1 - x - 8

\frac{( x ^{2} - 9 )}{( x - 3 )}

ab + mn + mb + an

125 a^{3} b^{3} - 343 c^{6}

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

What is factor 512x^6-27y^3z^9 ?
The solution to factor 512x^6-27y^3z^9 is (8x^2-3yz^3)(64x^4+24x^2yz^3+9y^2z^6)