Add, subtract, and multiply polynomials beyond quadratic cases.
Model a context with polynomial multiplication and simplify the expression
Problem
A box has dimensions \(x\), \(x~+~2\), and \(x~+~5\). Find its volume as a polynomial.
Big Picture
What this problem is really about
This is a volume problem before it is a polynomial problem: the three dimension expressions must be multiplied, not added. We’ll form the product of all three dimensions, multiply two factors first, and then distribute the remaining x. Simplifying that product gives a polynomial whose terms still represent cubic units.
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