What is the value of a^4-b^4?

[gmatstain]

I am having trouble with this data sufficiency problem. Any help is much appreciated. Thanks.

What is the value of a^4-b^4?

(1) a^2 - b^2 = 16
(2) a+b = 8

I factored a^4-b^4 down to (a^2-b^2)(a^2+b^2). So I thought that both were insufficient and chose answer E, but the answer is actually C. How can you use the 2 things they gave to derive a value? What am I missing in the factoring?

[Guest]

(1) a^2 - b^2 = 16
(2) a+b = 8
1 and 2
(a+b)(a-b) = 16 and a + b = 8
then a - b = 2
then a = 5 and b = 3
a^4 - b^4 = 5^4 - 3^4

[gmatstain]

Thank you for the response. I totally missed that relationship the first time I did the problem, but now I see it. Thanks!

[StaceyKoprince]

Thanks to the guest who provided the explanation. Make sure you write EVERYthing down, as sequentially and neatly as possible, and you will catch these little things more often than you miss them!