hi, I have been having some trouble doing this problem, could some one help me out?
If a+b=6, ab=4 find the value of a^3+b^3. (a+b)^3=a^3+3a^2b+3ab^2+b^3
I'm sorry if this is a bit unclear, the a^2 means a to the power of 2. thanks for the help.

Perhaps, try using the sum of two cubes factorization.



Then we get it down to

Did they give you by chance?

No they didn't, sorry, that was all that it said

Then we can finish by solving for a or b in the givens.

ab=4... [1]

a+b=6... [2]

From [1], a=4/b

Sub into [2]:

(4/b)+b=6



Now, can you finish up?

Yes, thank you for the help Galactus.

you may finish the solution #2 suggested by galacuts like this:
(a+b)^2=a^2 + b^2 + 2ab
36 = a^2+b^2 + 8 , therefore, a^2+b^2=28

now a^3+b^3 =(a+b)(a^2 + b^2 - ab)
=6 (28-4)=6(24)=144