What is factor 27x^6+8y^3 ?

The solution to factor 27x^6+8y^3 is (3x^2+2y)(9x^4-6x^2y+4y^2)

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factor 27x^6+8y^3

factor

27 x^{6} + 8 y^{3}

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

Solution steps

27 x^{6} + 8 y^{3}

Apply exponent rules

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

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

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

\frac{1}{8} + \frac{3}{20}

- 3 + 4 (a - 3 b + 2) - 5 (2 - a + 3 b)

\frac{( - 4 + 2 i )}{( 1 + i )}

3 a (2 b - 7)

- 17 + 2 (6 x - 1) + 5

What is factor 27x^6+8y^3 ?
The solution to factor 27x^6+8y^3 is (3x^2+2y)(9x^4-6x^2y+4y^2)