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Factor the expression: 3a - c - 3ab + bc

Mathematics

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Answer

(1 - b)(3a - C)

Step-by-step solution

4 steps
  1. Group the terms with common factors.

    We can group the first two terms and the last two terms, or group terms with 'a' and terms with 'c'. Let's group terms that share 3a3a and terms that share CC.

    3a−C−3ab+bC3a - C - 3ab + bC

    Rearrange the terms to group them more clearly:

    3a−3ab−C+bC3a - 3ab - C + bC
  2. Factor out the common factor from each group.

    From the first group, 3a−3ab3a - 3ab, the common factor is 3a3a.

    3a(1−b)3a(1 - b)

    From the second group, −C+bC-C + bC, the common factor is −C-C.

    −C(1−b)-C(1 - b)
  3. Combine the factored groups.

    Now the expression is:

    3a(1−b)−C(1−b)3a(1 - b) - C(1 - b)
  4. Factor out the common binomial factor (1−b)(1 - b).

    (1−b)(3a−C)(1 - b)(3a - C)
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