Answer
$16b^2+32b+16$
Work Step by Step
Using the square of a binomial, $(a+b)^2=a^2+2(a)(b)+b^2$, the given expression is equivalent to
\begin{align*}
&
[3+(4b+1)]^2
\\\\&
3^2+2(3)(4b+1)+(4b+1)^2
\\\\&
9+24b+6+(4b+1)^2
\\\\&
24b+15+(4b+1)^2
\\\\&
24b+15+(4b)^2+2(4b)(1)+1^2
\\\\&
24b+15+16b^2+8b+1
\\\\&
16b^2+(24b+8b)+(15+1)
\\\\&
16b^2+32b+16
.\end{align*}
