Factor 8y^2-200z^2

$8 y^{2} - 200 z^{2}$

Step 1

Factor $8$ out of $8 y^{2} - 200 z^{2}$ .

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

$8 (y^{2}) - 200 z^{2}$

Factor $8$ out of $- 200 z^{2}$ .

$8 (y^{2}) + 8 (- 25 z^{2})$

Factor $8$ out of $8 (y^{2}) + 8 (- 25 z^{2})$ .

$8 (y^{2} - 25 z^{2})$

Step 2

Rewrite $25 z^{2}$ as ${(5 z)}^{2}$ .

$8 (y^{2} - {(5 z)}^{2})$

Step 3

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

$8 ((y + 5 z) (y - (5 z)))$

Step 4

Factor.

Multiply $5$ by $- 1$ .

$8 ((y + 5 z) (y - 5 z))$

Remove unnecessary parentheses.

$8 (y + 5 z) (y - 5 z)$