The given expression can be written as [tex]q^{2} +12q+32[/tex] = (q+8)(q+4).
Step-by-step explanation:
Given,
[tex]q^{2} +12q+32[/tex]
To make it a complete square.
Formula
(a+b)² = [tex]a^{2} +2ab+b^{2}[/tex]
[tex]a^{2} -b^{2} = (a+b)(a-b)[/tex]
Now,
[tex]q^{2} +12q+32[/tex]
= [tex]q^{2} +2.q.6+6^{2} -6^{2} +32[/tex]
= (q+6)²-36+32
= (q+6)²-4
= (q+6)²-2²
= (q+6+2)(q+6-2)
= (q+8)(q+4)
