College Algebra 7th Edition

$4(t-\frac{5}{2}^{2})$
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. $4(t^{2}-5t+\frac{25}{4})=4(t-\frac{5}{2})^{2}$