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Message: Hi professor MG. I had a question about multiplying polynomials. I was wondering why we combine like terms for some and for others we distribute? The examples during lecture for that section shows both combining and distributing so I was confused.

Reply: When you're just adding or subtracting polynomials, you are working on combining like terms. Distribution comes into play whenever you have to multiply polynomials that have more than one term. You distribute the terms and then combine like terms afterwards. Examples from section 5.1 should be about combining like terms whereas the ones from 5.2 will probably have distribution first followed by combining like terms. If you're multiplying two monomials, however, then you're multiplying without distribution. So something like (8xy)(2xy) wouldn't require distribution to get 16x^2y^2 but something like (8x+y)(2x+y) would require distribution.