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Praxis Math · Question of the Day

Praxis Math Question of the Day

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Friday, October 23, 2026

When 5a3−45ab25a^3 - 45ab^2 is factored completely, which of the following is one of its factors?

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Question of the Day

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When 5a3−45ab25a^3 - 45ab^2 is factored completely, which of the following is one of its factors?

  1. (a−9b)(a - 9b)
  2. (a−3b)(a - 3b) (correct answer)
  3. 55
  4. (a2−9b2)(a^2 - 9b^2)

Explanation: First, identify the greatest common factor (GCF) of the terms. Both terms are divisible by 5a5a. Factoring out 5a5a gives 5a(a2−9b2)5a(a^2 - 9b^2). The term in the parentheses, a2−9b2a^2 - 9b^2, is a difference of squares, a2−(3b)2a^2 - (3b)^2, which factors into (a−3b)(a+3b)(a - 3b)(a + 3b). Therefore, the completely factored expression is 5a(a−3b)(a+3b)5a(a - 3b)(a + 3b). One of the factors is (a−3b)(a - 3b).