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

[mathdad]

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?

 

[MarkFL]

I would first write the expression as:

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

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

 

[mathdad]

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?

 

[MarkFL]

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:

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

 

[mathdad]

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.