1. ## Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

I'm having a hard time understanding how to go about simplifying this expression.
Should I use FOIL? I can't seem to find any videos or tutorials online with similar problems.

I have come close with the answer but I still don't get why the answer is x^(3b^2) not x^(-3b^2)

If anyone can offer some advice that would be much appreciated.

2. ## Re: Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

$\displaystyle (x^a)^b = x^{a\cdot b}$
$\displaystyle \dfrac{1}{x^a} = x^{-a}$

So, yes, you should FOIL the exponents.

3. ## Re: Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

Originally Posted by justincase13

I'm having a hard time understanding how to go about simplifying this expression.
Should I use FOIL? I can't seem to find any videos or tutorials online with similar problems.

I have come close with the answer but I still don't get why the answer is x^(3b^2) not x^(-3b^2)

If anyone can offer some advice that would be much appreciated.
well let's take a look

$\Large \dfrac{\left(x^{a+b}\right)^{a-b}}{\left(x^{a-2b}\right)^{a+2b}}=$

$\Large \dfrac {x^{(a+b)(a-b)}}{x^{(a-2b)(a+2b)}}=$

$\Large \dfrac{x^{a^2-b^2}}{x^{a^2-4b^2}}=$

$\Large \dfrac{x^{a^2}x^{-b^2}}{x^{a^2}x^{-4b^2}}=$

$\Large x^{3b^2}$

$\Large -b^2 - (-4b^2)=3b^2$

4. ## Re: Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

Thanks so much guys...can I also think of it like this ?

5. ## Re: Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

You cannot cancel the x's. The answer is

$\displaystyle x^{a^2-b^2}x^{-(a^2-4b^2)} = x^{a^2-b^2-(a^2-4b^2)} = x^{a^2-a^2+4b^2-b^2} = x^{3b^2}$

So, the $\displaystyle a^2$ cancels, but the $\displaystyle x$ does not.

6. ## Re: Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

Originally Posted by justincase13
Thanks so much guys...can I also think of it like this ?
don't cross out your x's, but yeah, I suppose you could look at it like that as long as you understand what it means.

7. ## Re: Need help with this algebra problem please... (x^a+b)^a-b/(x^a-2b)^a_2b

Originally Posted by justincase13

I'm having a hard time understanding how to go about simplifying this expression.
Should I use FOIL? I can't seem to find any videos or tutorials online with similar problems.

I have come close with the answer but I still don't get why the answer is x^(3b^2) not x^(-3b^2)

If anyone can offer some advice that would be much appreciated.
just multiply the exponents respectively

x^ [(a^2-b^2) -(a^2-4b^2)] = x^ 3b^2