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 Sum 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})

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

4 x y + 2 x z - 6 y - 3 z

a^{x - 1} b - b^{n - 1} a

- 5 x + 20 x + 2.1

6 m^{2} + 7 m^{2} - 20

+ (- \frac{1}{2})

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)