The following is from a practice GRE question. I was hoping if anyone could tell me if I have reached the right conclusion for the right reasons.
The question is as follows:
Given that ab = 0, which value is greater?
A) (a + b)^8
B) (a - b)^8
C) Answers A & B are equal
D) Cannot be determined
I calculated this as follows:
(a-b)^8 = ((a-b)^2)^4
= ((a^2 - 2ab + b^2))^4
= ((a^2 - 0 + b^2))^4
= (a^2 + b^2)^4
(a+b)^8 = ((a+b)^2)^4
= ((a^2 + 2ab + b^2))^4
= ((a^2 + 0 + b^2))^4
= (a^2 + b^2)^4
Therefore, A & B both evaluate to (a^2 + b^2)^4 and the correct answer is C.
An easier way to see this is that $ab = 0$ implies $a=0$ or $b=0$. In the first case you have $(0+b)^8 = (0-b)^8$. In the second case, $(a+0)^8 = (a-0)^8$.