Question

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

Answer 1

`=-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`

Answer 2

`- 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`