The total number of terms in the expansion of $(x+a)^{100} + (x-a)^{100}$ after simplification is:
🎥 Video solution / Text Solution of this question is given below:
$(x+a)^{100} = \sum_{r=0}^{100} \binom{100}{r} x^{100-r}a^r$
$(x-a)^{100} = \sum_{r=0}^{100} \binom{100}{r} x^{100-r}(-a)^r$
Adding, odd powers of $a$ cancel and even powers remain.
Even $r$: total even $r$ from 0 to 100 → 51 terms.