Prove polynomial identities and use them to solve or describe numerical relationships.
Verify a polynomial identity by expanding and comparing both sides
Problem
Verify \((x~+~2)^2~=~x^2~+~4x~+~4\) by expanding the left side.
Big Picture
What this problem is really about
An identity must agree for every input, so verify it by converting both sides to the same polynomial form. Rewrite the square as two identical binomials, distribute every term—including both cross products—and combine like terms. A term-by-term match then proves the identity, while a single numerical check by itself would only supply evidence.
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