Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Multiply two binomials and simplify the polynomial product
Problem
Multiply the binomials \((x~+~3)(x~+~5)\). Give the coefficients of the product in descending-degree order, including zeros for missing degrees.
Big Picture
What this problem is really about
Multiplying two binomials means accounting for all four pairwise products, including the two cross-products in the middle. We’ll distribute each term of the first factor across the second, combine the two linear terms, and then read the quadratic, linear, and constant coefficients in order.
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