# How do you simplify 4 – 3 [ 4 – 2 ( 6 – 3 ) ] + 2 using PEMDAS?

Start with the deepest bracket in, then work your way out and you'll eventually get to $12$

#### Explanation:

$4 - 3 \left[4 - 2 \left(6 - 3\right)\right] + 2$

The first place to start is with P - Parentheses (also known as brackets). There are 2 sets of parentheses, one set inside the other. So the one that is "deepest in" should be where we start:

$4 - 3 \left[4 - 2 \cdot 3\right] + 2$

We have one more set of P to do, but in this case we have 2 different operations inside that P. Do we do the multiplication first or the subtraction? We work our way down PEDMAS and see that D and M, division and multiplication, come before A and S (addition and subtraction), so let's multiply, then subtract:

$4 - 3 \left[4 - 6\right] + 2$

$4 - 3 \left[- 2\right] + 2$

Now we have choices again - we have subtraction, multiplication, and addition to choose from as to which to do first. As before, D and M come before A and S:

$4 - \left(- 6\right) + 2$

Now here's and interesting thing - we have a negative sign outside of a bracket, which is really just saying $\left(- 1\right) \left(- 6\right)$, which is multiplication, so that comes before the adding or subtracting:

$4 - \left(- 6\right) + 2$

$4 + 6 + 2 = 12$

Jul 14, 2016

12

#### Explanation:

The most important concept in simplifying any expression is to count the number of terms. (terms are separated by + and - signs.)

Each term must have an answer and only in the last step can these be added - working from left to right.

Within each term, work from the strongest operations (powers and roots, then multiply and divide, and the weakest operations are add and subtract. If you want to do a weaker operation first, it must be in brackets, and be done first.

$\textcolor{b l u e}{4} - \textcolor{m a \ge n t a}{3 \left[4 - 2 \left(6 - 3\right)\right]} + \textcolor{\lim e}{2} \text{ has 3 terms}$

There are 2 terms inside the square brackets.

=$\textcolor{b l u e}{4} - \textcolor{m a \ge n t a}{3 \left[\textcolor{b l a c k}{4} - \textcolor{\mathmr{and} a n \ge}{2 \left(6 - 3\right)}\right]} + \textcolor{\lim e}{2} \text{ }$ Work inside the orange brackets

=$\textcolor{b l u e}{4} - \textcolor{m a \ge n t a}{3 \left[\textcolor{b l a c k}{4} - \textcolor{\mathmr{and} a n \ge}{2 \left(3\right)}\right]} + \textcolor{\lim e}{2} \text{ }$ Find the answer for the orange brackets
=$\textcolor{b l u e}{4} - \textcolor{m a \ge n t a}{3 \left[\textcolor{b l a c k}{4} - \textcolor{\mathmr{and} a n \ge}{6}\right]} + \textcolor{\lim e}{2}$

=$\textcolor{b l u e}{4} - \textcolor{m a \ge n t a}{3 \left[- 2\right]} + \textcolor{\lim e}{2} \text{ }$ Answer for inside pink brackets.
=$\textcolor{b l u e}{4} \text{ "color(magenta)(+6]" } + \textcolor{\lim e}{2}$

There are now final answers for the 3 terms which can be added, work from left to right.

+$12$