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

2 Answers
Aug 23, 2017

#=-312#

Explanation:

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

Start with the innermost brackets and work outwards.

#color(blue)(12)-2{24+2[3color(red)((7+4))+color(red)((6)^2)]}#
#color(white)(wwwwwwwwwwww)darrcolor(white)(xxx)darr#
#=color(blue)(12)-2{24+2[3color(red)((11))+color(red)((36))]}#
#color(white)(wwwwwwwwwww)darr#
#=color(blue)(12)-2{24+2[color(red)(33)+36]}#

#=color(blue)(12)-2{24+2{color(lime)(33+36]}#
#color(white)(wwwwwwwwwwwww)darr#
#=color(blue)(12)-2{24" + "2color(lime)((69)}#
#color(white)(wwwwwwwww.www)darr#
#=color(blue)(12)-2{24" "+" "color(lime)(138]}#

#=color(blue)(12)-2{color(magenta)(24+138)]}#
#color(white)(wwwwwww)darr#
#=color(blue)(12)-2{color(magenta)(162)}#
#color(white)(wwwwwww)darr#
#=color(blue)(12)" "-color(magenta)(324)#

#=-312#

Aug 23, 2017

#- 312#

Explanation:

We have: #12 - 2 {24 + 2 [3 (7 + 4) + (6)^(2)]}#

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

"PEMDAS" is an acronym for:

#"Parentheses",# #"exponents",# #"multiplication,"# #"division",# #"addition"# #and# #"subtraction."#

First, let's evaluate the operations within parentheses:

#= 12 - 2 {24 + 2 [3 times 11 + 6^(2)]}#

Next, we evaluate any exponents:

#= 12 - 2 {24 + 2 [3 times 11 + 36]}#

Then, we perform any multiplication:

#= 12 - 2 {24 + 2 [33 + 36]}#

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

#= 12 - 2 {24 + 2 [69]}#

#= 12 - 2 {24 + 138}#

#= 12 - 2 {162}#

#= 12 - 324#

Finally, let's subtract the two numbers:

#= - 312#