Factor 8y^4+x^3y

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

Step 1

Factor $y$ out of $8 y^{4} + x^{3} y$ .

Factor $y$ out of $8 y^{4}$ .

$y (8 y^{3}) + x^{3} y$

Factor $y$ out of $x^{3} y$ .

$y (8 y^{3}) + y x^{3}$

Factor $y$ out of $y (8 y^{3}) + y x^{3}$ .

$y (8 y^{3} + x^{3})$

Step 2

Rewrite $8 y^{3}$ as ${(2 y)}^{3}$ .

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

Step 3

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = 2 y$ and $b = x$ .

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

Step 4

Factor.

Simplify.

Apply the product rule to $2 y$ .

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

Raise $2$ to the power of $2$ .

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

Multiply $2$ by $- 1$ .

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

Remove unnecessary parentheses.

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

Factor 8y^4+x^3y

Related Questions

Support LCMGCF.com by disabling your adblocker.