## Algebra 1: Common Core (15th Edition)

$(a+4b)(a+8b)$
$12$ is positive, so we list positive factors of $32$. $\left[\begin{array}{lll} \text{Factors of 32 } & \text{Sum of factors}1 \text{ and }32 & 33\\ 2\text{ and }16 & 18 & \\ 4\text{ and }8 & 12 & \text{...is what we need} \end{array}\right]$ $a^{2}+12ab+32b^{2}=(a+4b)(a+8b)$ Check: $(a+4b)(a+8b)=$ ...use the FOIL method. $=a^{2}+8ab+4ab+32b^{2}$ ...add like terms. $=a^{2}+12ab+32b^{2}$