These polynomials are multipled using the distributive property because they are monomials (no plus or minus signs) multiplied to binomials (one plus or minus sign).
There are different thought processes for multiplying the numbers and the letters. The numbers multiply just the same as they did in elementary school. The letters multiply by counting the number of occurances for each letter and using that count as an exponent. Here's a few examples to illustrate:
4xy(3x+2y) = 12 x^2 y + 8 x y^2 For the first term we multiplied 4xy and 3x. 4 times 3 is twelve, there are 2 x's getting us x ^2, and 1 y for y^1 (or just y), making 12 x^2 y. For the second term, 4 times 2 is 8, there is 1 x getting us x, and 2 y's getting us y^2, making 8 x y^2. The + sign in (3x+2y) moves into our answer, getting us
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