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.
Factoring an expression means to find the numbers or variables that can be multiplied together to get the original expression.
Factoring is important because it simplifies complex expressions, making them easier to work with and manipulate in mathematical and scientific calculations.
To factor an expression, you need to find common factors, use the distributive property, and apply any relevant factoring techniques such as the difference of squares or grouping.
Factoring involves breaking down an expression into its simpler components, while expanding involves multiplying out an expression to its expanded form.
No, not every expression can be factored. Some expressions may not have any common factors or may not be able to be simplified using any known factoring techniques.