Find twice the coefficient of \(a^2b^2\) in the expansion of \(\left(4a^2+9b^2\right)^2\).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 144
By \((p+q)^2=p^2+2pq+q^2\), the term with \(a^2b^2\) is the middle term \(2pq\).
\(p=4a^2\), \(q=9b^2\)
\(\left(4a^2+9b^2\right)^2=16a^4+2\times4a^2\times9b^2+81b^4=16a^4+72a^2b^2+81b^4\)
Coefficient of \(a^2b^2\) \(=72\)
Twice the coefficient \(=2\times72=144\)