Factoring by difference of two squares

[CosmicAnon]

instructions: factor each difference of two squares. Assume that any variable exponents represent whole numbers.
a^2 - (b-2)^2

My work:

a^2 -(b-2)(b+2)

I know the answer is (a+b-2)(a-b+2) I just don’t understand how to get there. Why is the a inside the parentheses? How did it get there?

 

[Deleted member 4993]

In your response, you expanded (b-2)^2 as (b-2)(b+2). That is incorrect. There is no need to expand (b-2)^2.

You need to use:

x^2 - y^2 = (x+y) * (x-y)

For your problem:

x = a

and

y = (b-2)

continue....

 

[Steven G]

Even if (b-2)^2 = (b+2)(b-2) you did not factor anything, you expanded things!