Expanding Brackets with a Fraction

• Apr 16th 2014, 12:03 AM
Katrena
Expanding Brackets with a Fraction
Attachment 30684

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?
• Apr 16th 2014, 12:14 AM
earboth
Re: Expanding Brackets with a Fraction
Quote:

Originally Posted by Katrena
Attachment 30684

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:

$\displaystyle 4x^2\left(\color{red}x+2+\frac1x \color{black}\right)=4x^2 \cdot \color{red}x + \color{black}4x^2 \cdot\color{red} 2 + \color{black}4x^2 \cdot \color{red}\frac1x \color{black} = \boxed{4x^3+8x^2+4x}$
• Apr 16th 2014, 12:23 AM
Katrena
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...
• Apr 16th 2014, 08:27 AM
JeffM
Re: Expanding Brackets with a Fraction
Quote:

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
• Apr 16th 2014, 10:24 AM
HallsofIvy
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
$\displaystyle 4x^2(x+ 2)$, you got $\displaystyle 4x^4+ 8x^3$. And that is not true!