Mathematics - Binomial Theorem Question with Solution | TestHub

To get common terms in both the expansions $\begin{array}{rlrl}& x^{r_1}{\left(y^2\right)}^{13-r_1}={\left(x^2\right)}^{r_2}(y{)}^{14-r_2}& r_1=2r_2\&26-2r_1=14-r_2& r_1=8;r_2=4\end{array}$ ∴ Only one term is common. ∴ Number of distinct terms $=14+15-1=28$