How do you simplify 12 - 2 {24 + 2 [3 (7 + 4) + (6)^(2)]}?

Aug 23, 2017

$= - 312$

Explanation:

There are only 2 terms. The first is already in its simplest form.
Simplify the second term:

$\textcolor{b l u e}{12} - 2 \left\{24 + 2 \left[3 \textcolor{red}{\left(7 + 4\right)} + \textcolor{red}{{\left(6\right)}^{2}}\right]\right\}$
$\textcolor{w h i t e}{w w w w w w w w w w w w} \downarrow \textcolor{w h i t e}{\times x} \downarrow$
$= \textcolor{b l u e}{12} - 2 \left\{24 + 2 \left[3 \textcolor{red}{\left(11\right)} + \textcolor{red}{\left(36\right)}\right]\right\}$
$\textcolor{w h i t e}{w w w w w w w w w w w} \downarrow$
$= \textcolor{b l u e}{12} - 2 \left\{24 + 2 \left[\textcolor{red}{33} + 36\right]\right\}$

=color(blue)(12)-2{24+2{color(lime)(33+36]}
$\textcolor{w h i t e}{w w w w w w w w w w w w w} \downarrow$
=color(blue)(12)-2{24" + "2color(lime)((69)}
$\textcolor{w h i t e}{w w w w w w w w w . w w w} \downarrow$
$= \textcolor{b l u e}{12} - 2 \left\{24 \text{ "+" } \textcolor{\lim e}{138}\right\}$

=color(blue)(12)-2{color(magenta)(24+138)]}
$\textcolor{w h i t e}{w w w w w w w} \downarrow$
$= \textcolor{b l u e}{12} - 2 \left\{\textcolor{m a \ge n t a}{162}\right\}$
$\textcolor{w h i t e}{w w w w w w w} \downarrow$
$= \textcolor{b l u e}{12} \text{ } - \textcolor{m a \ge n t a}{324}$

$= - 312$

Aug 23, 2017

$- 312$

Explanation:

We have: $12 - 2 \left\{24 + 2 \left[3 \left(7 + 4\right) + {\left(6\right)}^{2}\right]\right\}$

Let's apply the "PEMDAS" rules for operator precedence.

"PEMDAS" is an acronym for:

$\text{Parentheses} ,$ $\text{exponents} ,$ $\text{multiplication,}$ $\text{division} ,$ $\text{addition}$ $\mathmr{and}$ $\text{subtraction.}$

First, let's evaluate the operations within parentheses:

$= 12 - 2 \left\{24 + 2 \left[3 \times 11 + {6}^{2}\right]\right\}$

Next, we evaluate any exponents:

$= 12 - 2 \left\{24 + 2 \left[3 \times 11 + 36\right]\right\}$

Then, we perform any multiplication:

$= 12 - 2 \left\{24 + 2 \left[33 + 36\right]\right\}$

There is no division in this case, so let's perform any addition:

$= 12 - 2 \left\{24 + 2 \left[69\right]\right\}$

$= 12 - 2 \left\{24 + 138\right\}$

$= 12 - 2 \left\{162\right\}$

$= 12 - 324$

Finally, let's subtract the two numbers:

$= - 312$