Prove polynomial identities and use them to solve or describe numerical relationships.
Expand a binomial square completely
Problem
Expand \((a~+~b)^2\) completely.
Big Picture
What this problem is really about
Squaring a binomial means multiplying two complete copies, so the expansion must account for every pair of terms. Distribute the first term across both terms, repeat with the second term, and then combine the two matching cross products. That organization prevents the common error of keeping only the two square terms.
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