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

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

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factor 27x^6+y^3

factor

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

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

Solution steps

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

Apply exponent rules

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

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

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

18 x^{8} - 9 x^{7} y^{4} + 27 y^{9}

3 x y - x^{2} y - 3 x y^{2}

2 m^{2} + 13 m + 20

20 a^{2} b^{4}

\frac{7 6}{14}

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