What is factor x^3y^6-8z^9 ?

The solution to factor x^3y^6-8z^9 is (xy^2-2z^3)(x^2y^4+2xy^2z^3+4z^6)

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factor x^3y^6-8z^9

factor

x^{3} y^{6} - 8 z^{9}

(x y^{2} - 2 z^{3}) (x^{2} y^{4} + 2 x y^{2} z^{3} + 4 z^{6})

Solution steps

x^{3} y^{6} - 8 z^{9}

Rewrite

x^{3} y^{6}

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

Rewrite

8 z^{9}

(2 z^{3})^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

= (x y^{2} - 2 z^{3}) (x^{2} y^{4} + 2 x y^{2} z^{3} + 4 z^{6})

y^{(4)}

\frac{d}{d y} ((x) (x^{2}))

β (1.1)

x + y + 3 x z + 3 yz

y^{12} - 8

What is factor x^3y^6-8z^9 ?
The solution to factor x^3y^6-8z^9 is (xy^2-2z^3)(x^2y^4+2xy^2z^3+4z^6)