Answer
$4(t-\frac{5}{2}^{2})$
Work Step by Step
First, factor out $4$ from the trinomial to rid the $t^{2}$ coefficient.
$4t^{2}-20t+25=4(t^{2}-5t+\frac{25}{4})$
Then, use the formula $a^{2}\pm2ab+b^2=(a\pm b)^{2}$ to factor the perfect square.
$4(t^{2}-5t+\frac{25}{4})=4(t-\frac{5}{2})^{2}$
