The discussion centers on the factorization of the expression 4a²b² - 9(ab + c)² from Precalculus by David Cohen, 3rd Edition, Chapter 1, Section 1.3, Question 29c. Participants confirm that expanding the quantity (ab + c) is unnecessary for factorization, as the expression can be recognized as a difference of squares: (2ab)² - (3(ab + c))². The factorization proceeds with the substitution of x = 2ab and y = 3(ab + c), leading to the factors (2ab - 3(ab + c))(2ab + 3(ab + c)). While further simplification is not required, some participants suggest it is good practice to simplify when possible.
PREREQUISITESStudents studying precalculus, educators teaching algebraic concepts, and anyone looking to enhance their skills in polynomial factorization.
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.