How do you simplify #x+ (x+2)#?

It is important to combine the like terms in expressions such as this #x + (x +2)#.

Like terms have the same variable raised to the same power, such as #2x^4# and #-4x^4#.

You can combine the like terms (or "add") them to each other. In this case, we have two #x#'s and a 2. The two #x#'s are like terms, as they are the same variable (x) and are raised to the same power (which is 1 although it is not shown).

You can combine the two #x#'s by #x + x = 2x#. The number 2 does not have any other terms that it can be considered as like terms, therefore we just leave that alone.

Our answer is: #2x + 2#

There is an extremely important reason why I do what I am about to do. It helps understanding!

Write as: #" "x+1(x+2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is the same as: #color(blue)(x + 1xx(x+2))#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Multiply everything inside the brackets by (+1) giving:

#x+x+2#

So we have 2 of #x# with the value of 2 added giving

#2x+2#

#color(blue)("~~~~~~~~~~~~~ Explaining the idea ~~~~~~~~~~~~~~~~~~~~")#

Suppose the question had been different and we had instead #x-(x+2)#

Write as #x -1(x+2)#

Multiply everything inside the bracket by #(-1)# giving

#x-x-2" "->" " 0-2" "->" "2#

#color(red)("By adopting method I did I was emphasising how to handle"##color(red)("the sign immediately to the left of the brackets.")#