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

1 Answer
Mar 20, 2016

You can not simplify this expression!
See 'discussion'


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.