# Question #964f3

Aug 14, 2014

These are the same expressions, just written differently. To prove this, just multiply the terms out and you'll end up with the same expression.

Let's start by multiplying the first equation:

${\left(x + 1\right)}^{3} - 5 x - 5$
$= \left(x + 1\right) \left(x + 1\right) \left(x + 1\right) - 5 x - 5$
$= \left({x}^{2} + 2 x + 1\right) \left(x + 1\right) - 5 x - 5$
$= {x}^{3} + {x}^{2} + 2 {x}^{2} + 2 x + x + 1 - 5 x - 5$
$= {x}^{3} + 3 {x}^{2} - 2 x - 4$

Now let's do the second equation:

$\left(x + 1\right) \left({x}^{2} + 2 x - 4\right)$
$= {x}^{3} + {x}^{2} + 2 {x}^{2} + 2 x - 4 x - 4$
$= {x}^{3} + 3 {x}^{2} - 2 x - 4$

As you can see, these are the same!