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

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

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factor x^6-8y^6

factor

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

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

Solution steps

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

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

64 a^{3} + 20 a - 125 b^{3} - 25 b

2 x^{2} - 2 x - 5 = 0

5 x + 3 = - 3 x - 1

\frac{n - 9}{n + 9} - \frac{n - 10}{n + 8}

am x^{2} + bm x y - an x y - bn y^{2}

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