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

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

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

factor

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

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

Solution steps

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

Rewrite

x^{6} y^{3}

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

Rewrite

27 z^{3}

(3 z)^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

l (t sinh (t))

25 a u - 10 a v + 5 xu - 2 xv

cos^{2} (a) + 2 cos (a) + 1

\frac{x ^{2} + 8 x + 16}{x + 4}

[x] + 1

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