Factor 25v^2-49

$25 v^{2} - 49$

Step 1

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

${(5 v)}^{2} - 49$

Step 2

Rewrite $49$ as $7^{2}$ .

${(5 v)}^{2} - 7^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 v$ and $b = 7$ .

$(5 v + 7) (5 v - 7)$