Question

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

Answer 1

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 `4x^2+3x^2`

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

As `(0)^3+(0)^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(1+x)`.

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.