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Factor 99-45f+36b to identify the equivalent expressions. Choose 2 answers: (A) 9(11-5f+4b) (B) 3(33-15+12) (C) 11(9-4f+3b) (D) 3(33-15 f+12 b)

Factor 99−45f+36b99-45 f+36 b to identify the equivalent expressions.\newlineChoose 22 answers:\newline(A) 9(11−5f+4b)9(11-5f+4b)\newline(B) 3(33−15+12)3(33-15+12)\newline(C) 11(9−4f+3b)11(9-4f+3b)\newline(D) 3(33−15f+12b)3(33-15 f+12 b)

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Full solution

Q. Factor 99−45f+36b99-45 f+36 b to identify the equivalent expressions.\newlineChoose 22 answers:\newline(A) 9(11−5f+4b)9(11-5f+4b)\newline(B) 3(33−15+12)3(33-15+12)\newline(C) 11(9−4f+3b)11(9-4f+3b)\newline(D) 3(33−15f+12b)3(33-15 f+12 b)
  1. Look for common factor: First, look for a common factor in 9999, −45f-45f, and 36b36b.
  2. Identify common factor: The common factor is 99.
  3. Factor out the common factor: Factor out the 99: 9(11−5f+4b)9(11 - 5f + 4b).
  4. Check options: Check the options to see which ones are equivalent to 9(11−5f+4b)9(11 - 5f + 4b).
  5. Option A match: Option A is 9(11−5f+4b)9(11 - 5f + 4b), which matches our factored expression.
  6. Option B incorrect: Option B is 3(33−15+12)3(33 - 15 + 12), but it doesn't have the variables ff and bb, so it's incorrect.
  7. Option C not equivalent: Option C is 11(9−4f+3b)11(9 - 4f + 3b), which is not equivalent because the coefficients do not match those in our factored expression.
  8. Option D correct: Option D is 3(33−15f+12b)3(33 - 15f + 12b), which simplifies to 99−45f+36b99 - 45f + 36b, so it's also correct.

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