Factor Quadratic Trinomials with Leading Coefficient 1: example 7.26

$\begin{array}{cccc}& & & x^2+12xy+36y^2\hfill \\ \begin{array}{c}\text{Note that the first terms are}x,\text{last terms}\hfill \\ \text{contain}y.\hfill \end{array}\hfill & & & \left(x\_y\right)\left(x\_y\right)\hfill \end{array}$

Find the numbers that multiply to 36 and add to 12.

$\begin{array}{cccc}\text{Use 6 and 6 as the coefficients of the last terms.}\hfill & & & \hfill \left(x+6y\right)\left(x+6y\right)\hfill \\ \text{Check your answer.}\hfill & & & \\ \\ \\ \left(x+6y\right)\left(x+6y\right)\hfill & & & \\ x^2+6xy+6xy+36y^2\hfill & & & \\ x^2+12xy+36y^2✓\hfill & & & \end{array}$