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)}-

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) (Show Source): You can put this solution on YOUR website!

The answer isn't because is not equal to .
Let a=3, b=2, and c=1 to show a counter-example.
.
.
So, the two expressions are not the same.
To solve the problem you first notice that .
What is useful here is that .
So, .
You can pull out a factor of (2x)^y from the equation. You then get
which is the answer the sample test gave.
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