To multiply two fractions, we simply multiply the numerators of the two fractions together and the denominators of the two fractions together to create one larger fraction. This is modeled as follows:
(q+5)(4q)/(2)(q+4)
Next, we must multiply out both the expressions in parentheses together in both the numerator and denominator to simplify.
4q^2 + 20q/2q + 8
The GCF, or greatest common factor, that is shared between both the numerator and the denominator is 2, which is what we should factor out in order to further simplify this fraction.
2 (2q^2 + 10q) / 2 (q + 4)
The 2 in the numerator and the 2 in the denominator "cancel" each other out, which leaves us with our final answer:
2q^2 + 10q / q + 4
We know that the above fraction is our final answer because there are no more shared factors between the numerator and the denominator that we can cancel out.
Hope this helps!