We want to factor any polynomials when we're multiplying to see if any common factors can be canceled out (the same on top and bottom) to simplify the multiplication process. You could still potentially get the correct answer in the end if you don't cancel out common factors, but your simplification at the end would be much more labor intensive with higher degree polynomials. Once all of the common factors have been canceled out, we multiply across the top, multiply across the bottom, and simplify. Domain restrictions are any values of variables that would make any denominators equal to zero, since dividing by zero is undefined.
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