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Simplify p(p - q) - q(q - p).
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first expand the brackets \[p*p =p^2 and p*(-q) =-pq\] and for the other bracket \[-q*q =-q^2 and (-q )*(-p) =pq\] therefore it is \[p^2-pq-q^2+pq\]now cross out what ever you can cross out at the end you are left with \[p^2-q^2\]
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