MHB How Do You Factor the Fractional Expression [(a + b)^2]/4 - [a^2b^2]/9?

[mathdad]

Factor [(a + b)^2]/4 - [a^2b^2]/9

Can someone get me started?

 

[MarkFL]

I would write the expression as the difference of squares:

$$\frac{(a+b)^2}{4}-\frac{a^2b^2}{9}=\left(\frac{a+b}{2}\right)^2-\left(\frac{ab}{3}\right)^2$$

Or, we could write:

$$\frac{(a+b)^2}{4}-\frac{a^2b^2}{9}=\frac{1}{36}\left(\left(3(a+b)\right)^2-(2ab)^2\right)$$

Now apply the difference of squares formula...:D

 

[mathdad]

Great. I can take it from here.