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Find the product. Simplify your answer. \newlinep2(3p24p)p^2(-3p^2 - 4p)

Full solution

Q. Find the product. Simplify your answer. \newlinep2(3p24p)p^2(-3p^2 - 4p)
  1. Distribute p2p^2: We need to distribute p2p^2 to both terms inside the parentheses: 3p2-3p^2 and 4p-4p.\newlinep2(3p24p)=p2(3p2)+p2(4p)p^2(-3p^2 - 4p) = p^2(-3p^2) + p^2(-4p)
  2. Simplify 3p2-3p^2: Now, let's simplify p2(3p2)p^2(-3p^2).\newlineMultiply p2p^2 and 3p2-3p^2.\newlinep2(3p2)=3p(2+2)=3p4p^2(-3p^2) = -3p^{(2+2)} = -3p^4
  3. Simplify 4p-4p: Next, simplify p2(4p)p^2(-4p).\newlineMultiply p2p^2 and 4p-4p.\newlinep2(4p)=4p2+1=4p3p^2(-4p) = -4p^{2+1} = -4p^3
  4. Combine results: Combine the results from the previous steps to get the final simplified expression. \newlinep2(3p24p)=3p44p3p^2(-3p^2 - 4p) = -3p^4 - 4p^3

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