Factoring by difference of two squares

CosmicAnon

New member
Joined
Mar 20, 2018
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1
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?
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,135
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....
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
3,018
Even if (b-2)^2 = (b+2)(b-2) you did not factor anything, you expanded things!
 
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