Factor 8y^3-50y

$8 y^{3} - 50 y$

Step 1

Factor $2 y$ out of $8 y^{3} - 50 y$ .

Factor $2 y$ out of $8 y^{3}$ .

$2 y (4 y^{2}) - 50 y$

Factor $2 y$ out of $- 50 y$ .

$2 y (4 y^{2}) + 2 y (- 25)$

Factor $2 y$ out of $2 y (4 y^{2}) + 2 y (- 25)$ .

$2 y (4 y^{2} - 25)$

Step 2

Rewrite $4 y^{2}$ as ${(2 y)}^{2}$ .

$2 y ({(2 y)}^{2} - 25)$

Step 3

Rewrite $25$ as $5^{2}$ .

$2 y ({(2 y)}^{2} - 5^{2})$

Step 4

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 y$ and $b = 5$ .

$2 y ((2 y + 5) (2 y - 5))$

Remove unnecessary parentheses.

$2 y (2 y + 5) (2 y - 5)$