Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.
Find a specific term in the expansion of \((a+b)^n\)
Problem
Find the third term of the expansion of \((x~+~2)^5\).
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What this problem is really about
Term position and the Binomial Theorem’s index are offset by one because indexing begins at zero. Convert the requested position to k first, then substitute k into the general term before simplifying. Keep the combination, the first term’s decreasing power, and the second term’s increasing power together so no numerical factor is lost.
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