# Thread: Factor and Simplify Algebraic Expression

1. ## Factor and Simplify Algebraic Expression

Factor and simplify each algebraic expression.

(4x - 1)1/2 - 1/3(4x - 1)3/2

2. ## Re: Factor and Simplify Algebraic Expression

Originally Posted by PaperStSoap
Factor and simplify each algebraic expression.

(4x - 1)1/2 - 1/3(4x - 1)3/2
Take the factor (4x-1)^1/2 out of both parts. Get (4x-1)^1/2[1-1/3(4x-1)] etc

3. ## Re: Factor and Simplify Algebraic Expression

could you further explain. I still have problems understanding why (4x - 1)1/2 - 1/3(4x - 1)3/2 = (4x-1)1/2[1-1/3(4x-1)].

4. ## Re: Factor and Simplify Algebraic Expression

nevermind, figured it out, feeling real stupid right now... could you explain what to do from here.

5. ## Re: Factor and Simplify Algebraic Expression

Originally Posted by PaperStSoap
nevermind, figured it out, feeling real stupid right now... could you explain what to do from here.
Can you simplify $\displaystyle 1 - \frac13\left(4x - 1\right)?$

6. ## Re: Factor and Simplify Algebraic Expression

I have no idea.

7. ## Re: Factor and Simplify Algebraic Expression

Originally Posted by PaperStSoap
I have no idea.
Are you familiar with the distributive property? Distribute the $\displaystyle \textstyle\frac13$ and combine like terms.

8. ## Re: Factor and Simplify Algebraic Expression

so it comes out to 1 - 4/3x + 1/3 (4x - 1)^1/2

9. ## Re: Factor and Simplify Algebraic Expression

Originally Posted by PaperStSoap
so it comes out to 1 - 4/3x + 1/3 (4x - 1)^1/2
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 $\displaystyle \textstyle1+\frac13?$

10. ## Re: Factor and Simplify Algebraic Expression

so far i got...
(4x - 1)^1/2 (-4x/3 + 4/3)
then i simplified (-4x/3 + 4/3) = -4x+4/3 = -4(x-1)/3
so the it would be (4x-1)^1/2 * -4(x-1) = -4(4x-1)^1/2(x-1)

11. ## Re: Factor and Simplify Algebraic Expression

Originally Posted by PaperStSoap
Factor and simplify each algebraic expression.
(4x - 1)1/2 - 1/3(4x - 1)3/2
Try this: let a = 4x - 1 ; then expression becomes:
a^(1/2) - a*a^(1/2) / 3

= [3a^(1/2) - a*a^(1/2)] / 3

= a^(1/2)(3 - a) / 3

continue...

12. ## Re: Factor and Simplify Algebraic Expression

Originally Posted by PaperStSoap
(4x - 1)^1/2 (-4x/3 + 4/3)
then i simplified (-4x/3 + 4/3) = -4x+4/3 = -4(x-1)/3
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.

Originally Posted by PaperStSoap
so the it would be (4x-1)^1/2 * -4(x-1) = -4(4x-1)^1/2(x-1)
What happened to the 3?

13. ## Re: Factor and Simplify Algebraic Expression

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

14. ## Re: Factor and Simplify Algebraic Expression

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

$\displaystyle -\frac43(x-1)(4x-1)^{1/2}$

$\displaystyle -\frac43(x-1)\sqrt{4x-1}.$