Factor 20y^4-45y^2

$20 y^{4} - 45 y^{2}$

Step 1

Factor $5 y^{2}$ out of $20 y^{4} - 45 y^{2}$ .

Factor $5 y^{2}$ out of $20 y^{4}$ .

$5 y^{2} (4 y^{2}) - 45 y^{2}$

Factor $5 y^{2}$ out of $- 45 y^{2}$ .

$5 y^{2} (4 y^{2}) + 5 y^{2} (- 9)$

Factor $5 y^{2}$ out of $5 y^{2} (4 y^{2}) + 5 y^{2} (- 9)$ .

$5 y^{2} (4 y^{2} - 9)$

Step 2

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

$5 y^{2} ({(2 y)}^{2} - 9)$

Step 3

Rewrite $9$ as $3^{2}$ .

$5 y^{2} ({(2 y)}^{2} - 3^{2})$

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 $b = 3$ .

$5 y^{2} ((2 y + 3) (2 y - 3))$

Remove unnecessary parentheses.

$5 y^{2} (2 y + 3) (2 y - 3)$