Factor 25y^2-4

$25 y^{2} - 4$

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

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

Rewrite $4$ as $2^{2}$ .

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

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

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