Does the trinomial fit the perfect square trinomials pattern, $a^2+2ab+b^2$?

• Is the first term a perfect square? Write it as a square, $a^2$.
Is $36g^2$ a perfect square?
Yes — write it as ${\left(6g\right)}^2$.

$\begin{array}{ccccc}36g^2& +& 60g& +& 25\\ {\left(6g\right)}^2& & & & \end{array}$

• Is the last term a perfect square? Write it as a square, $b^2$.
Is $25$ a perfect square?
Yes — write it as $5^2$.

$\begin{array}{ccccc}36g^2& +& 60g& +& 25\\ {\left(\text{}6g\text{}\right)}^2& & & & {\left(\text{}5\text{}\right)}^2\end{array}$

• Check the middle term. Is it $2ab$?
Is $60g$ twice the product of $6g$ and $5$?

$\begin{array}{ccccc}36g^2& +& 60g& +& 25\\ {\left(\text{}6g\text{}\right)}^2& & & & {\left(\text{}5\text{}\right)}^2\\ & & 2·\left(6g\right)·5& & \\ & & 60g& & \end{array}$

Does it match?
Yes, so we have a perfect square trinomial!

Write it as the square of a binomial.

$36g^2+60g+25$

$\begin{array}{ccccc}{a}^2& +& 2·a·b& +& b^2\\ {\left(6g\right)}^2& +& 2·\left(6g\right)·5& +& 5^2\end{array}$

$\begin{array}{ccccc}(& a& +& b& {)}^2\\ (& 6g& +& 5& {)}^2\end{array}$

$\begin{array}{c}{(\text{}a\text{}+\text{}b\text{})}^2\\ {(\text{}6g\text{}+\text{}5\text{})}^2\end{array}$

Check.

${\left(6g+5\right)}^2$

${\left(6g\right)}^2+2·6g·5+5^2$

$36g^2+60g+25$ ✓