SOLUTION: hi, i just took the practice SAT on collegeboard.com, and one problem really stumped me. here it is: (2x)^(3y) - (2x)^y the answer that was given was: (2x)^y [{(2x)^(2y)}-

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: hi, i just took the practice SAT on collegeboard.com, and one problem really stumped me. here it is: (2x)^(3y) - (2x)^y the answer that was given was: (2x)^y [{(2x)^(2y)}-      Log On


   

Question 63648: hi, i just took the practice SAT on collegeboard.com, and one problem really stumped me. here it is:
(2x)^(3y) - (2x)^y
the answer that was given was:
(2x)^y [{(2x)^(2y)}-1]
i may or may not have typed the answer incorrectly, i don't know how to. :P
what i thought was the answer was: (2x)^2y
why not?
Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%29%5E%283y%29+-+%282x%29%5Ey
The answer isn't %282x%29%5E%282y%29 because a%5Eb+-+a%5Ec is not equal to a%5E%28b-c%29.
Let a=3, b=2, and c=1 to show a counter-example.
a%5Eb-a%5Ec+=+3%5E2-3%5E1+=+9-3+=+6.
a%5E%28b-c%29+=+3%5E%282-1%29+=+3%5E1+=+3.
So, the two expressions are not the same.
To solve the problem you first notice that 3y+=+2y%2By.
What is useful here is that a%5E%28b%2Bc%29+=+%28a%5Eb%29%28a%5Ec%29.
So, .
You can pull out a factor of (2x)^y from the equation. You then get
+%28%282x%29%5Ey%29%28%282x%29%5E%282y%29+-+1%29%29 which is the answer the sample test gave.