Apply the binomial theorem (a+b)ⁿ = sum_k=0ⁿ nk aⁿ-k b^k with a=x, b=2y, and n=5.

Here are the solutions to the problems:

1. Find the binomial expansion of $(x+2y)^5$.

Step 1: Apply the binomial theorem $(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$ with $a=x$, $b=2y$, and $n=5$.

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