When multiplying fractions, we multiply across the top, multiply across the bottom, and reduce. The same is true if you're multiplying a fraction times a polynomial- put the polynomial over one so you can be clear what will be in the resulting numerator and what will be the the denominator. Factor everything, so you'll be working with parentheses factors rather than trying to multiply x^2 times x^2 and getting higher exponents. Once things are totally factored, you can cross out any factors that are the same in top and bottom.
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