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

Apr 16, 2016

$2 x + 2$

#### Explanation:

It is important to combine the like terms in expressions such as this $x + \left(x + 2\right)$.

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

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 $x + x = 2 x$. 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: $2 x + 2$

Apr 16, 2016

$2 x + 2$

#### Explanation:

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

Write as: $\text{ } x + 1 \left(x + 2\right)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is the same as: $\textcolor{b l u e}{x + 1 \times \left(x + 2\right)}$
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Multiply everything inside the brackets by (+1) giving:

$x + x + 2$

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

$2 x + 2$

$\textcolor{b l u e}{\text{~~~~~~~~~~~~~ Explaining the idea ~~~~~~~~~~~~~~~~~~~~}}$

Suppose the question had been different and we had instead $x - \left(x + 2\right)$

Write as $x - 1 \left(x + 2\right)$

Multiply everything inside the bracket by $\left(- 1\right)$ giving

$x - x - 2 \text{ "->" " 0-2" "->" } 2$

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