# Thread: Expanding Brackets with a Fraction

1. ## Expanding Brackets with a Fraction

The answer is: 4x³ +8x² +4x

So clearly I have done this incorrectly as I put the answer as '4x^4 +8x³ +4x²'

You can probably guess what I've done wrong, as I thought I had to remove the fraction by multiplying all the terms by the denominator.
It seems as though everything is multiplied as though the fraction isn't there. What am I supposed to do?

2. ## Re: Expanding Brackets with a Fraction

Originally Posted by Katrena

The answer is: 4x³ +8x² +4x

So clearly I have done this incorrectly as I put the answer as '4x^4 +8x³ +4x²'

You can probably guess what I've done wrong, as I thought I had to remove the fraction by multiplying all the terms by the denominator.
It seems as though everything is multiplied as though the fraction isn't there. What am I supposed to do?
Good morning,

you have to distribute the factor to the summands here:

$4x^2\left(\color{red}x+2+\frac1x \color{black}\right)=4x^2 \cdot \color{red}x + \color{black}4x^2 \cdot\color{red} 2 + \color{black}4x^2 \cdot \color{red}\frac1x \color{black} = \boxed{4x^3+8x^2+4x}$

3. ## Re: Expanding Brackets with a Fraction

Okay, thanks for quick reply. So I guess I just put the 4x² as a fraction, over a 1 and multiply with the 1/x...

4. ## Re: Expanding Brackets with a Fraction

Originally Posted by Katrena
Okay, thanks for quick reply. So I guess I just put the 4x² as a fraction, over a 1 and multiply with the 1/x...
Correct

5. ## Re: Expanding Brackets with a Fraction

It looks to me like the fraction is not really the problem. Ignoring the fraction you appear to be saying that for
$4x^2(x+ 2)$, you got $4x^4+ 8x^3$. And that is not true!