What is factor x^6-8y^3 ?

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

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factor x^6-8y^3

factor

x^{6} - 8 y^{3}

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

Solution steps

x^{6} - 8 y^{3}

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

10 x^{2} + 3 - 9 x^{2} + 4 x + 1

450 \div \frac{7}{8}

\frac{16}{( - 4 )}

(x + 10) (x - 9)

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