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

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

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

factor

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

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

Solution steps

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

Rewrite

x^{3} y^{3}

(x y)^{3}

Rewrite

27 z^{3}

(3 z)^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(x y - 3 z) ((x y)^{2} + 3 z x y + (3 z)^{2}) : (x y - 3 z) (x^{2} y^{2} + 3 x yz + 9 z^{2})

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

a x - a y - b x + b y - c x + cy

lo g_{a} (x^{2} - 64)

3 b z + 6 a^{2} b - 18 a b^{2} - a z

[3.3]

36 + (5 tan^{2} (6 x))

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