Concept: Binomial expansion: The binomial expansion of the sum a and b to the power n is: (a+b)n=nC1anb0+nC2an−1b1+...+nCna0bn Calculation: We will substitute a = x2 and b = y2 . We can write the first bracket as follows: (a+b)25=25C1a25b0+25C2a24b1+...+25C25a0b25 Similarly, we can write the second bracket as follows: (a+b)25=25C1a25b0−25C2a24b1+...+25C25a0b25 If we add both the equations we observe that all the even terms will get cancelled and we will only left with the odd-numbered terms. There are total 13 terms in the first bracket and identical 13 terms from the second bracket. Therefore, total number of terms in the expression will be 13.