Factoring

[CLEP101]

I know this is proabably easy for you math gurus, but can someone break this one down for me. What is the answer and how do you get it.

Which of the following is a factor of 36 – (a – b)2?

a. 36 + a – b

b. 6 + a – b

c. 6 – a – b

d. a – b

e. – (a – b)2

[gcalvin]

The factors of a^2 - b^2 are (a + b) and (a - b). In other words:

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

Therefore, the factors of 36 - (a - b)^2 are (6 + (a - b)) and (6 - (a - b)). That means that only answer (b) is correct. (The other factor would simplify to "6 - a + b", not "6 - a - b" as in answer ©.)

Hope that helps.

-Gary-