Find three times the coefficient of \(m^2n^2\) in the expansion of \(\left(5m^2+7n^2\right)^2\).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 210
By \((p+q)^2=p^2+2pq+q^2\), the term with \(m^2n^2\) is the middle term \(2pq\).
\(p=5m^2\), \(q=7n^2\)
\(\left(5m^2+7n^2\right)^2=25m^4+2\times5m^2\times7n^2+49n^4=25m^4+70m^2n^2+49n^4\)
Coefficient of \(m^2n^2\) \(=70\)
Three times the coefficient \(=3\times70=210\)