# How do you factor 9t^2+42t+49?

May 1, 2016

$9 {t}^{2} + 42 t + 49 = {\left(3 t + 7\right)}^{2}$
Notice that $9 {t}^{2} = {\left(3 t\right)}^{2}$ and $49 = {7}^{2}$ are both perfect squares, so it remains to check whether the middle term is correct:
${\left(3 t + 7\right)}^{2} = {\left(3 t\right)}^{2} + 2 \left(3 t\right) \left(7\right) + {7}^{2} = 9 {t}^{2} + 42 t + 49$