What is factor 27x^3y^6+z^9 ?

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

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factor 27x^3y^6+z^9

factor

27 x^{3} y^{6} + z^{9}

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

Solution steps

27 x^{3} y^{6} + z^{9}

Rewrite

27 x^{3} y^{6}

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

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

Apply exponent rule:

a^{b c} = (a^{b})^{c}

z^{9} = (z^{3})^{3}

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

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

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

4 a - 3 a c + 8 b - 6 b c

\frac{1}{1 + e ^{10}}

3 a x + a - 15 b x - 5 b

(b + c) - a

x^{2} - \frac{3}{2} x + 1

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