Answer
$q^2+\frac{3}{2}q+\frac{9}{16}$
Work Step by Step
RECALL:
$(a+b)(a+b) = a^2+2ab+b^2$
Use the formula above with $a=q$ and $b=\frac{3}{4}$ to obtain:
$(q+\frac{3}{4})(q+\frac{3}{4})
\\=q^2 +2(q)(\frac{3}{4})+(\frac{3}{4})^2
\\=q^2+\frac{3}{2}q+\frac{9}{16}$
