The number of distinct terms in the expansion of  ${(x+y^2)}^{13}+{(x^2+y)}^{14}$ is _______

To get common terms in both the expansions $x^{r_1}{\left(y^2\right)}^{13-r_1}={\left(y\right)}^{14-r_2}{\left(x^2\right)}^{r_2}$

$$\begin{gathered} \therefore r_1=2r_{2}and26-2r_1=14-r_2 \\ \therefore r_1=8,r_2=4 \end{gathered}$$

Only one term is common.