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Factor 18 p-36 to identify the equivalent expressions. Choose 2 answers: A 3(9p-12) B 9(2p-4p) c 2(9p-18) D 18(p-2)

Factor 18p−36 18 p-36 to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 3(9p−12) 3(9 p-12) \newlineB 9(2p−4p) 9(2 p-4 p) \newlinec 2(9p−18) 2(9 p-18) \newlineD 18(p−2) 18(p-2)

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Full solution

Q. Factor 18p−36 18 p-36 to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 3(9p−12) 3(9 p-12) \newlineB 9(2p−4p) 9(2 p-4 p) \newlinec 2(9p−18) 2(9 p-18) \newlineD 18(p−2) 18(p-2)
  1. Identify GCF: First, we need to identify the greatest common factor (GCF) of the terms 18p18p and 3636. The GCF of 18p18p and 3636 is 1818 since 1818 is the largest number that divides both terms without a remainder.
  2. Factor Out GCF: Now, we factor out the GCF from each term. This gives us:\newline18p−36=18(p)−18(2)18p - 36 = 18(p) - 18(2)
  3. Simplify Expression: Simplify the expression inside the parentheses to get the factored form: 18(p)−18(2)=18(p−2)18(p) - 18(2) = 18(p - 2)
  4. Check Options: Now, let's check the given options to see which ones are equivalent to the factored expression 18(p−2)18(p - 2).\newlineOption A: 3(9p−12)=27p−363(9p - 12) = 27p - 36, which is not equivalent to 18(p−2)18(p - 2) because 27p27p is not the same as 18p18p.\newlineOption B: 9(2p−4p)=9(−2p)9(2p - 4p) = 9(-2p), which is not equivalent to 18(p−2)18(p - 2) because the sign and coefficients do not match.\newlineOption C: 2(9p−18)=18p−362(9p - 18) = 18p - 36, which is equivalent to 18(p−2)18(p - 2) because when we distribute the 22, we get the original expression.\newlineOption D: 18(p−2)18(p - 2) is the same as the factored expression we found, so it is equivalent.\newlineTherefore, the correct options are C and D.

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