Factor and simplify each algebraic expression.
(4x - 1)^{1/2} - 1/3(4x - 1)^{3/2}
You need to be more careful with your parentheses, but that otherwise looks okay.
$\displaystyle (4x-1)^{1/2} - \frac13(4x-1)^{3/2}$
$\displaystyle =(4x-1)^{1/2}\left[1 - \frac13(4x-1)\right]$
$\displaystyle =(4x-1)^{1/2}\left(1 - \frac43x + \frac13\right)$
Now what is $\displaystyle \textstyle1+\frac13?$
Again, you need to watch your parentheses. It took me a moment to realize that "-4x+4/3" was supposed to mean $\displaystyle \textstyle\frac{-4x+4}3$ and not $\displaystyle \textstyle-4x+\frac43,$ which is how you wrote it.
What happened to the 3?
i forgot to divide the the whole thing by three. so my final answer, which is also wrong according to my book, is
-4(4x-1)^1/2(x-1)
the answer in the book is 4(4x-1)^1/2(x-1).
What's tripping me up is why mine starts with -4. I must be doing something wrong when simplifying [1-1/3(4x-1)]
where i did 1 - 1/3(4x) + 1/3(1)=
1 - 4x/3 + 1/3 =
3/3 - 4x/3 + 1/3 =
-4x/3 - (3/3 + 1/3) =
(-4x - 4)/3 =
-4(x-1)/3
Look very carefully at the original problem to make sure you've copied correctly. Is this the expression that you were given?
$\displaystyle (4x - 1)^{1/2} - \frac13(4x - 1)^{3/2}$
And is this the exact answer that is written in the book?
$\displaystyle 4(4x-1)^{1/2}(x-1)$
If so, your book is in error. The correct answer would be
$\displaystyle -\frac43(x-1)(4x-1)^{1/2}$
or, in radical form,
$\displaystyle -\frac43(x-1)\sqrt{4x-1}.$