## Precalculus (6th Edition)

$(2p+q-5)^{2}$
Test whether this is a perfect square, $(A-B)^{2}=A^{2}-2AB+B^{2}$ First term: $A^{2}=(2p+q)^{2}\Rightarrow A=2p+q$ Third term: $B^{2}=(5)^{2}\Rightarrow B=5$ Test:$\qquad$ does $-2AB$ equal the middle term? $-2AB=-2(2p+q)(5)=-10(2p+q)\qquad$ ... yes, it does. $\Rightarrow$This is a perfect square, $[(2p+q)-5]^{2}=(2p+q-5)^{2}$