Question

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

Answer 1

`2x + 2`

Explanation:

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`

Answer 2

`2x+2`

Explanation:

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.")`