To simplify the expression [tex]\(|2-5| - (12 \div 4 - 1)^2\)[/tex], we will follow these steps in a detailed manner:
1. Calculate the absolute value:
- Evaluate [tex]\(2 - 5\)[/tex]: This results in [tex]\(-3\)[/tex].
- Take the absolute value of [tex]\(-3\)[/tex]: [tex]\(|-3| = 3\)[/tex].
2. Simplify the expression inside the parentheses:
- Start with the division: [tex]\(12 \div 4\)[/tex] equals [tex]\(3\)[/tex].
- Subtract 1 from the result of the division: [tex]\(3 - 1 = 2\)[/tex].
3. Square the result of the subtraction:
- Square [tex]\(2\)[/tex]: [tex]\(2^2 = 4\)[/tex].
4. Subtract the squared result from the absolute value calculated at the beginning:
- Subtract [tex]\(4\)[/tex] from [tex]\(3\)[/tex]: [tex]\(3 - 4 = -1\)[/tex].
Hence, the simplified value of the expression [tex]\(|2-5| - (12 \div 4 - 1)^2\)[/tex] is [tex]\(-1\)[/tex].
