What is factor 8x^6-27y^6 ?

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

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factor 8x^6-27y^6

factor

8 x^{6} - 27 y^{6}

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

Solution steps

8 x^{6} - 27 y^{6}

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

(2 x + 3) (x + 4) = 0

- 3

- 3 g + 6 = 9 g^{2}

\frac{y + 1}{4} - \frac{y}{3} > 1 + \frac{2 y - 1}{6}

7 x - 3 = 32

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