Factorising

**dankelly07** · January 19th 2009, 12:48 AM

I need help factorising..

Nk+1 = Nk + rNk(1-Nk/k)

= (1+r -Nk/k)Nk

Apparently that equals..

= (1+r)[1-Nk/(1+r)k]Nk

But i dont see how...

**mr fantastic** · January 19th 2009, 02:38 AM

Originally Posted by dankelly07

I need help factorising..

Nk+1 = Nk + rNk(1-Nk/k)

= (1+r -Nk/k)Nk

Apparently that equals..

= (1+r)[1-Nk/(1+r)k]Nk

But i dont see how...

$N_k + r N_k \left(1 - \frac{N_k}{k} \right)$

$= N_k \left[ 1 + r \left(1 - \frac{N_k}{k} \right) \right]$

$= N_k \left[ 1 + r - \frac{r N_k}{k} \right]$

$= N_k \left[ (1 + r) - \frac{r N_k}{k} \right]$

$= N_k (1 + r) \left[1 - \frac{{\color{red}r} N_k}{k (1 + r)} \right]$

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