1. simplifying help

Can someone please explain, how $\displaystyle \frac{k^{2}(k+1)^{2} +4(k+1)^{3}}{4}$ simplifies to

$\displaystyle \frac{({k+1}^{2})k^{2}+4(k+1)}}{{4}}$

2. Re: simplifying help

Originally Posted by Tweety
Can someone please explain, how $\displaystyle \frac{k^{2}(k+1)^{2} +4(k+1)^{3}}{4}$ simplifies to

$\displaystyle \frac{({k+1}^{2})k^{2}+4(k+1)}}{{4}}$
Well it does not!

$\displaystyle \frac{k^{2}(k+1)^{2} +4(k+1)^{3}}{4}=\frac{(k+1)^{2}[k^{2} +4(k+1)]}{4}=\frac{(k+1)^{2}[(k+2)^2]}{4}$

3. Re: simplifying help

Originally Posted by Plato
Well it does not!

$\displaystyle \frac{k^{2}(k+1)^{2} +4(k+1)^{3}}{4}=\frac{(k+1)^{2}[k^{2} +4(k+1)]}{4}=\frac{(k+1)^{2}[(k+2)^2]}{4}$
but your second expression is exactly the same as my second expression. I know it simplifies to your last expression, but I dont understand the second part.

4. Re: simplifying help

Originally Posted by Tweety
but your second expression is exactly the same as my second expression. I know it simplifies to your last expression, but I dont understand the second part.
No it is not.
Look at the grouping symbol $\displaystyle [~~]$

5. Re: simplifying help

I think I got it, we factor out a (k+1) term, from $\displaystyle (k+1)^{2}$ and from $\displaystyle (k+1)^{3}$

6. Re: simplifying help

Make your life easier: remove the division by 4; let x = k+1