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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?

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:

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

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...

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

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!