Simplify using the order of operations, make sure to show all your work. 3 − 5(1 − 22)2 + 8÷2 × 2
To simplify the expression using the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), we perform the calculations in the following steps:
1) First, we calculate the expression inside the parentheses: 1 - 22 = -21.
Therefore, the expression becomes: 3 - 5(-21)² + 8÷2 × 2.
2) Next, we perform the exponentiation: (-21)² = (-21) × (-21) = 441.
Thus, the expression simplifies to: 3 - 5(441) + 8÷2 × 2.
3) Then, we perform multiplication: 5 × 441 = 2205.
Thus, the expression becomes: 3 - 2205 + 8÷2 × 2.
4) After that, we perform division: 8 ÷ 2 = 4.
Therefore, the expression simplifies to: 3 - 2205 + 4 × 2.
5) Next, we perform multiplication: 4 × 2 = 8.
Thus, the expression becomes: 3 - 2205 + 8.
6) Finally, we perform the subtraction and addition in order: 3 - 2205 = -2202, and -2202 + 8 = -2194.
Therefore, the simplified expression is -2194.