Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.
Find a requested coefficient in a binomial expansion
Problem
Find the coefficient of \(x^3\) in \((x~+~2)^5\).
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What this problem is really about
Work backward from the requested variable power to identify k. Set the first term’s exponent n minus k equal to the target exponent, solve for k, and then form only that Binomial Theorem term. When extracting the coefficient, include both the combination and any powered numerical constant, but leave out the variable factor itself.
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