What is factor x^3y^6+27z^{42} ?

The solution to factor x^3y^6+27z^{42} is (xy^2+3z^{14})(x^2y^4-3xy^2z^{14}+9z^{28})

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factor x^3y^6+27z^{42}

factor

x^{3} y^{6} + 27 z^{42}

(x y^{2} + 3 z^{14}) (x^{2} y^{4} - 3 x y^{2} z^{14} + 9 z^{28})

Solution steps

x^{3} y^{6} + 27 z^{42}

Rewrite

x^{3} y^{6}

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

Rewrite

27 z^{42}

(3 z^{14})^{3}

= (x y^{2})^{3} + (3 z^{14})^{3}

Apply Sum of Cubes Formula:

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

(x y^{2})^{3} + (3 z^{14})^{3} = (x y^{2} + 3 z^{14}) ((x y^{2})^{2} - 3 z^{14} x y^{2} + (3 z^{14})^{2})

= (3 z^{14} + x y^{2}) ((3 z^{14})^{2} - 3 z^{14} x y^{2} + (x y^{2})^{2})

Simplify

(x y^{2} + 3 z^{14}) ((x y^{2})^{2} - 3 z^{14} x y^{2} + (3 z^{14})^{2}) : (x y^{2} + 3 z^{14}) (x^{2} y^{4} - 3 x y^{2} z^{14} + 9 z^{28})

= (x y^{2} + 3 z^{14}) (x^{2} y^{4} - 3 x y^{2} z^{14} + 9 z^{28})

5 x^{2} y - 5 x^{2} + x y - x + y - 1

(x + 1) (x - 3) (x + 4) (x - 6) + 38

(x + 3)^{2} - 17

- 8 π x y^{3} - 10 π y^{3}

x^{y} y^{x} + x y + x^{y + 1} + y^{x + 1}

What is factor x^3y^6+27z^{42} ?
The solution to factor x^3y^6+27z^{42} is (xy^2+3z^{14})(x^2y^4-3xy^2z^{14}+9z^{28})