What is factor 27x^3y^3-8z^6 ?

The solution to factor 27x^3y^3-8z^6 is (3xy-2z^2)(9x^2y^2+6xyz^2+4z^4)

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factor 27x^3y^3-8z^6

factor

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

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

Solution steps

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

Rewrite

27 x^{3} y^{3}

(3 x y)^{3}

Rewrite

8 z^{6}

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

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

2 π r^{2} + 2 π r

sin (2 t - 12)

- 2 x^{5} + 6

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

(3 x^{2}) - 2

What is factor 27x^3y^3-8z^6 ?
The solution to factor 27x^3y^3-8z^6 is (3xy-2z^2)(9x^2y^2+6xyz^2+4z^4)