# How do you simplify x^3 + x^4?

Mar 20, 2016

You can not simplify this expression!
See 'discussion'

#### Explanation:

You can not add these directly as they have different values rather than being counts of the same value; as you would get in $4 {x}^{2} + 3 {x}^{2}$

The only case when you could add them is if $x = 0$

As ${\left(0\right)}^{3} + {\left(0\right)}^{4} = 0 + 0 = 0$

This particular idea about adding zeros is perhaps a falsehood as: how can you add nothing to nothing. Adding in one sense means 'put with' or 'combine'. As this usually results in a change in total value, no value change has occurred!

The only way to change this is to factor out as many $x ' s$ as you can. Resulting in: ${x}^{3} \left(1 + x\right)$.

However, I view this as making it more complicated so I suggest:

You can not simplify this expression!

On the other hand; if you knew what $x$ was 'worth' then you could add those values.