Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Rewrite a polynomial expression in simplified standard form by carrying out operations and combining like terms by degree
Problem
Multiply \((x~+~4)(x~-~2)\), combine like terms, and write the resulting polynomial in simplified standard form.
Big Picture
What this problem is really about
To put this product in standard form, every term in one binomial has to multiply every term in the other. We’ll form all four pairwise products, keep careful track of the negative factor, combine the two linear terms, and arrange the remaining terms from greatest power to least.
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