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Factor 60-36 w to identify the equivalent expressions. Choose 2 answers: A 6(10-6w) B 4(15-8w) C 12(5-3w) D 3(20+12 w)

Factor 60−36w 60-36 w to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 6(10−6w) 6(10-6 w) \newlineB 4(15−8w) 4(15-8 w) \newlineC 12(5−3w) 12(5-3 w) \newlineD 3(20+12w) 3(20+12 w)

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Full solution

Q. Factor 60−36w 60-36 w to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 6(10−6w) 6(10-6 w) \newlineB 4(15−8w) 4(15-8 w) \newlineC 12(5−3w) 12(5-3 w) \newlineD 3(20+12w) 3(20+12 w)
  1. Determine GCF of 6060 and −36w-36w: Determine the Greatest Common Factor (GCF) of 6060 and −36w-36w.\newlineThe GCF of 6060 and 3636 is 1212, and since we are also factoring out a variable ww, the GCF of 6060 and −36w-36w is −36w-36w00.
  2. Write factored form using GCF: Write 60−36w60 - 36w in the factored form using the GCF.\newlineThe factored form of 60−36w60 - 36w is 12(5−3w)12(5 - 3w).
  3. Compare with given choices: Compare the factored form with the given choices to identify the equivalent expressions.\newlineThe factored form we found is 12w(5−3w)12w(5 - 3w), but we need to compare it with the given choices without the variable ww, as the choices are in terms of 60−36w60 - 36w, not 60w−36w260w - 36w^2. Therefore, the correct factored form to compare is 12(5−3w)12(5 - 3w).
  4. Choose equivalent expressions: Choose the equivalent expressions for 60−36w60 - 36w from the given choices.\newlineLooking at the choices:\newlineA) 6(10−6w)6(10 - 6w) is not equivalent because 66 is not the GCF.\newlineB) 4(15−8w)4(15 - 8w) is not equivalent because 44 is not the GCF and the factors are incorrect.\newlineC) 12(5−3w)12(5 - 3w) is equivalent because it matches the factored form we found.\newlineD) 3(20+12w)3(20 + 12w) is not equivalent because the sign of the second term is positive and the factors are incorrect.
  5. Confirm correct choices: Confirm the correct choices.\newlineThe correct choices that are equivalent to the factored expression of 60−36w60 - 36w are:\newlineC) 12(5−3w)12(5 - 3w)

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