Aspire Faculty ID #13842 · Topic: JAMIA MILLIA ISLAMIA MCA 2021 · Just now
JAMIA MILLIA ISLAMIA MCA 2021

The total number of terms in the expansion of $(x+a)^{100} + (x-a)^{100}$ after simplification is:

Solution

$(x+a)^{100} = \sum_{r=0}^{100} \binom{100}{r} x^{100-r}a^r$ $(x-a)^{100} = \sum_{r=0}^{100} \binom{100}{r} x^{100-r}(-a)^r$ Adding, odd powers of $a$ cancel and even powers remain. Even $r$: total even $r$ from 0 to 100 → 51 terms.
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