How do you simplify 4times3^2+3times4^2+2(3times4)^2?

Aug 6, 2016

$4 \times {3}^{2} + 3 \times {4}^{2} + 2 {\left(3 \times 4\right)}^{2} = 372$

Explanation:

The order of operations is given by PEMDAS, which means parentheses, exponents, multiplication and division and addition and subtraction in that order.

Hence, $4 \times {3}^{2} + 3 \times {4}^{2} + 2 {\left(3 \times 4\right)}^{2}$

= $4 \times {3}^{2} + 3 \times {4}^{2} + 2 \times {12}^{2}$

= $4 \times 9 + 3 \times 16 + 2 \times 144$

= $36 + 48 + 288$

= $372$

Aug 6, 2016

$372$

Explanation:

Blindly following PEDMAS/BODMAS/PEMDAS or any other version, without understanding what it actually means, will often lead to incorrect answers.

Strongest operations (powers and roots) are done first, then multiplication and division, and lastly the weakest operations of addition and subtraction.

However, sometimes a weaker operation must be done first and in this case parentheses are used.

Count the number of terms first. You can perform operations in any term independent of other terms. Each term must simplify to a single value. The final values are added and subtracted in the LAST step.

$\textcolor{red}{4 \times {3}^{2}} \textcolor{b l u e}{+ 3 \times {4}^{2}} \textcolor{g r e e n}{+ 2 {\left(3 \times 4\right)}^{2}} \text{ has 3 terms}$

=$\textcolor{red}{4 \times 9} \textcolor{b l u e}{+ 3 \times 16} \textcolor{g r e e n}{+ 2 {\left(12\right)}^{2}}$

=color(red)(36)color(blue)(+48)color(green)(+2(144)

=$\textcolor{red}{36} \textcolor{b l u e}{+ 48} \textcolor{g r e e n}{+ 288}$

=$372$

Jan 18, 2017

372

Explanation:

PEMDAS

Parentheses
Exponents
Multiplication
Division
$4 \cdot {3}^{2} + 3 \cdot {4}^{2} + 2 {\left(3 \cdot 4\right)}^{2}$
$4 \cdot {3}^{2} + 3 \cdot {4}^{2} + 2 \cdot {12}^{2}$
$4 \cdot 9 + 3 \cdot 16 + 2 \cdot 144$
$36 + 48 + 288$
$376$