# How do you simplify 5 + 2 (2 times 3)^2 - 7 + 8 ÷ 4(5 - 3) using order of operations?

Sep 27, 2016

$74$

#### Explanation:

In simplifying expressions with different operations, it is important to count the number of terms first. EAch term will simplify to a single answer and they will be added or subtracted in the last step.
Within each term, parentheses get done first, followed by powers and roots, then multiply and divide.

You can work in different terms in the same line.

color(lime)(5)color(darkblue)( + 2 (2 times 3)^2) color(red)(- 7)color(mediumpurple)( + 8 ÷ 4(5 - 3))" "larr  there are 4 terms

=color(lime)(5)color(darkblue)( + 2 (6)^2) color(red)(- 7)color(mediumpurple)( + 8 ÷ 4(2))

$= \textcolor{\lim e}{5} \textcolor{\mathrm{da} r k b l u e}{+ 2 \left(36\right)} \textcolor{red}{- 7} \textcolor{m e \mathrm{di} u m p u r p \le}{+ 2 \left(2\right)}$

$= \textcolor{\lim e}{5} \textcolor{\mathrm{da} r k b l u e}{+ 72} \textcolor{red}{- 7} \textcolor{m e \mathrm{di} u m p u r p \le}{+ 4} \text{ } \leftarrow$ move the subtract to the end

$= \textcolor{\lim e}{5} \textcolor{\mathrm{da} r k b l u e}{+ 72} \textcolor{m e \mathrm{di} u m p u r p \le}{+ 4} \textcolor{red}{- 7}$

$= 74$