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

1 Answer
Mar 20, 2016

Answer:

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.