Question

-81p^2+18pq-q^2

Answer 1

\[-(q-9 p)^2 \]

Answer 2

Mind telling me how you got that?

Answer 3

\[-81p^2+18pq-q^2=-(81p^2-18pq+q^2)\]
We know that \[(a-b)^2=a^2-2ab+b^2\]
We try \[a^2=81p^2 \Rightarrow a=9p\]
\[b^2=q^2 \Rightarrow b=q\]
We verify \[2ab=2(9p)q=18pq\]
So \[-(81p^2-18pq+q^2)=-(q-9p)^2\]