Can I Factor 4a^2b^2 - 9(ab + c)^2?

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SUMMARY

The expression 4a²b² - 9(ab + c)² can be factored using the difference of squares method. The first step involves rewriting the expression as (2ab)² - (3(ab + c))². This allows for the application of the difference of squares formula, leading to the simplified result. It is crucial to recognize that the number 9 is not part of the squaring of (ab + c)², but rather represents 3², which is essential for proper factorization.

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mathdad
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Factor the expression.

4a^2b^2 - 9(ab + c)^2

Should I FOIL (ab + c)^2 as step 1?

I can then distribute 9 as step 2, right?
 
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I would first write the expression as:

$$(2ab)^2-(3(ab+c))^2$$

Now, factor as the difference of squares, and simplify. :D
 
MarkFL said:
I would first write the expression as:

$$(2ab)^2-(3(ab+c))^2$$

Now, factor as the difference of squares, and simplify. :D

The number 9 is not part of the squaring for (ab + c)^2. So, where did 3 come from? Does 3 come from the fact that 3^2 is 9? This makes sense to me if 9 were inside the parentheses for (ab + c)^2 but it's not. See what I mean?
 
RTCNTC said:
The number 9 is not part of the squaring for (ab + c)^2. So, where did 3 come from? Does 3 come from the fact that 3^2 is 9? This makes sense to me if 9 were inside the parentheses for (ab + c)^2 but it's not. See what I mean?

I was just rewriting that term as a perfect square:

$$9(ab+c)^2=3^2(ab+c)^2=(3(ab+c))^2$$
 
MarkFL said:
I was just rewriting that term as a perfect square:

$$9(ab+c)^2=3^2(ab+c)^2=(3(ab+c))^2$$

Ok. I will complete this problem tomorrow.
 

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