What is the coefficient on the $x^{135}$ term in the expansion of $\left(2+x^3\right)^{100}$?
I solved a similar question, but my method isn't working when the second term in the expansion is raised to a power other than 1.
2026-03-31 18:18:07.1774981087
Binomial Expansion, finding specific coefficient
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The binomial theorem tells us that $$(a + b)^n = \sum_{k = 1}^n {{n}\choose{k}} a^kb^{n-k}.$$
Here $a = 2$ and $b = x^3$. Solve for what $k$ needs to be for the $x^{135}$ term, and then ${{n}\choose{k}} a^k$ will be your coefficient! Let me know if you need any more help!