The discussion revolves around the process of factoring the expression 4a^2b^2 - 9(ab + c)^2 from a precalculus textbook. Participants explore whether it is necessary to expand the quantity (ab + c) before proceeding with the factorization.
Participants express differing views on the necessity of expanding the quantity before factoring, with some advocating for direct factorization and others emphasizing the potential benefits of simplification. No consensus is reached on the best approach.
Participants acknowledge that while they have factored the expression, the discussion remains open regarding the appropriateness of further simplification and the interpretation of the problem's requirements.
RTCNTC said:Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 29c.
Factor the expression.
4a^2b^2 - 9(ab + c)^2
Must I expand the quantity (ab + c) before factoring?
RTCNTC said:(2ab)^2−(3(ab+c))^2
I will let 2ab = x and [3(ab + c)] = y.
x^2 - y^(2)
(x - y)(x + y)
Back-substitute now.
[(2ab - 3(ab + c)][(2ab + 3(ab + c)]
Correct?
RTCNTC said:I thought about distributing within the factors and combining like terms but the question is asking to factor not to simplify after factoring.
MarkFL said:Well, technically, further simplification is not required to complete the goal of factorization...you have indeed factored...but in my opinion, it's just good practice to simplify whenever possible.