Factor x^3+2x^2y-4x-8y

$x^{3} + 2 x^{2} y - 4 x - 8 y$

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

$(x^{3} + 2 x^{2} y) - 4 x - 8 y$

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $x + 2 y$ .

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

Rewrite $4$ as $2^{2}$ .

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

Factor.

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Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$(x + 2 y) ((x + 2) (x - 2))$

Remove unnecessary parentheses.

$(x + 2 y) (x + 2) (x - 2)$

Factor x^3+2x^2y-4x-8y

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