Let's simplify the expression [tex]\( |3 - 10| - (12 \div 4 + 2)^2 \)[/tex] step-by-step.
1. Calculate the absolute value:
[tex]\[ |3 - 10| \][/tex]
The absolute value of a number is its distance from 0 on the number line, regardless of direction. Therefore, the calculation is:
[tex]\[ 3 - 10 = -7 \][/tex]
[tex]\[ | -7 | = 7 \][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[ 12 \div 4 + 2 \][/tex]
First, perform the division:
[tex]\[ 12 \div 4 = 3 \][/tex]
Then add 2 to the result:
[tex]\[ 3 + 2 = 5 \][/tex]
3. Square the result from the parentheses:
[tex]\[ 5^2 \][/tex]
Squaring means multiplying the number by itself:
[tex]\[ 5^2 = 25 \][/tex]
4. Subtract the squared value from the absolute value:
[tex]\[ 7 - 25 \][/tex]
Perform the subtraction:
[tex]\[ 7 - 25 = -18 \][/tex]
Thus, the simplified result is [tex]\( -18 \)[/tex].
The correct answer is:
[tex]\[ -18 \][/tex]
