# How do you simplify 4 + 8 * |8 - (8 - 2)^2|  using order of operations?

Apr 17, 2018

$4 + 8 \setminus \cdot | 8 - {\left(8 - 2\right)}^{2} |$

$= 4 + 8 \cdot | 8 - {6}^{2} |$

$= 4 + 8 \setminus \cdot | 8 - 36 |$

$= 4 + 8 \setminus \cdot | - 28 |$

$= 4 + 8 \setminus \cdot 28$

$= 4 + 224$

$= 228$

Apr 17, 2018

See explanation.

#### Explanation:

The order of operation can be rememberd through an acronym PEDMAS. The letters in the acronym stand for:

P - Parenetheses (also called brackets)

E - Exponents

D and M - Division and Multiplication

A and S - Addition and Subtraction

The acronym says that first you need to do all operations in brackets (parenetheses). Here you have two kinds of brackets: ordinary brackets ( and ), but also absolute value signs $| |$ (these are also considered as brackets). First we need to perform operations in these brackets which do not include other ones (the most inner)

In the given expression the brackets without other ones are $\left(8 - 2\right)$, so we have to do this subtraction first:

$4 + 8 \cdot | 8 - {\textcolor{red}{\left(8 - 2\right)}}^{2} | = 4 + 8 \cdot | 8 - {\textcolor{red}{6}}^{2} |$

Now the expression in brackets is $| 8 - {6}^{2} |$. This includes power (square) and subtraction. According to the acronym you have to calculate the powers first, so the result will be:

$4 + 8 \cdot | 8 - \textcolor{red}{{6}^{2}} | = 4 + 8 \cdot | 8 - \textcolor{red}{36} |$

Now we have a subtraction inside the absolute value to perform:

$4 + 8 \cdot | \textcolor{red}{8 - 36} | = 4 + 8 \cdot | \textcolor{red}{- 28} |$

Now the absolute value contains only a number $- 28$, so to proceed we have to calculate the absolut value. As the expression in absolute value sign is negative, the value is opposite, so we have:

$4 + 8 \cdot \textcolor{red}{| - 28 |} = 4 + 8 \cdot \textcolor{red}{28}$

Now we do not have any brackets, so we can look at the operations. On the list below the brackets we have exponents, but there are none in the expression, next is division and multiplication. We have the multiplication, so we have to do it next:

$4 + \textcolor{red}{8 \cdot 28} = 4 + \textcolor{red}{224}$

Finally we have only addition which is our last operation to perform:

$4 + 224 = 228$

Answer: The value of the expression is $228$.