Question
Solve:
$ 25-p^2-q^2-2 p q $
$ 25-p^2-q^2-2 p q $
✓
Answer
$ 25-p^2-q^2-2 p q $
$ =25-\left(p^2+2 p q+q^2\right) $
$ =5^2-\left(p^2+2 \times p \times q+q^2\right) $
$ =5^2-(p+q)^2 $
$ =[5-(p+q)][5+(p+q)] $
$ =(5-p+q)(5+p+q) $
$ =-(p+q-5)(p+q+5) $
$ =25-\left(p^2+2 p q+q^2\right) $
$ =5^2-\left(p^2+2 \times p \times q+q^2\right) $
$ =5^2-(p+q)^2 $
$ =[5-(p+q)][5+(p+q)] $
$ =(5-p+q)(5+p+q) $
$ =-(p+q-5)(p+q+5) $
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