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Which of the following is the sum of p-2 and (p+3)(p-6) ? Choose 1 answer: (A) 3p-5 (B) 2p^(2)-20 (C) p^(2)-2p-20 (D) p^(3)-5p^(2)-12 p+36

Which of the following is the sum of p−2 p-2 and (p+3)(p−6) (p+3)(p-6) ?\newlineChoose 11 answer:\newline(A) 3p−5 3 p-5 \newline(B) 2p2−20 2 p^{2}-20 \newline(C) p2−2p−20 p^{2}-2 p-20 \newline(D) p3−5p2−12p+36 p^{3}-5 p^{2}-12 p+36

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Q. Which of the following is the sum of p−2 p-2 and (p+3)(p−6) (p+3)(p-6) ?\newlineChoose 11 answer:\newline(A) 3p−5 3 p-5 \newline(B) 2p2−20 2 p^{2}-20 \newline(C) p2−2p−20 p^{2}-2 p-20 \newline(D) p3−5p2−12p+36 p^{3}-5 p^{2}-12 p+36
  1. Expand Expression: First, we need to expand the expression (p+3)(p−6)(p+3)(p-6) using the distributive property (also known as the FOIL method for binomials).\newline(p+3)(p−6)=p⋅p+p⋅(−6)+3⋅p+3⋅(−6)(p+3)(p-6) = p\cdot p + p\cdot(-6) + 3\cdot p + 3\cdot(-6)\newline=p2−6p+3p−18= p^2 - 6p + 3p - 18\newline=p2−3p−18= p^2 - 3p - 18
  2. Combine Terms: Now, we add the expanded expression to the other term, p−2p-2. \newlineSum = (p−2)+(p2−3p−18)(p-2) + (p^2 - 3p - 18)\newline= p2−3p+p−2−18p^2 - 3p + p - 2 - 18\newline= p2−2p−20p^2 - 2p - 20
  3. Check Calculations: We check our calculations to ensure there are no math errors. The terms have been combined correctly, and the arithmetic is accurate.

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