Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Expand a binomial product using a special-product pattern
Problem
Apply a special-product pattern to expand \((x~+~5)^{2}\). State the pattern, identify its substituted quantities, and give the expanded polynomial.
Big Picture
What this problem is really about
Because the same sum is multiplied by itself, this is a square-of-a-sum pattern. We’ll use a squared plus two a b plus b squared, match a with x and b with five, and simplify the three resulting terms; the doubled middle product is what keeps the linear term from disappearing.
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