Simplify using the order of operations, make sure to show all your work. 3 − 5(1 − 2^2)^2 + 8÷2 × 2 (2 points)
To simplify the expression using the order of operations, we will follow the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, inside the parentheses, we have 1 − 2^2. Exponents take priority, so we must calculate 2^2 first.
2^2 = 4
Now we can substitute the value back into the expression:
3 − 5(1 − 4)^2 + 8÷2 × 2
Next, we have the exponent outside the parentheses:
(1 - 4)^2 = (-3)^2 = 9
Now we can substitute again:
3 − 5(9) + 8÷2 × 2
Now we can perform the multiplication and division from left to right:
3 − 45 + 8÷2 × 2
Next, we perform the multiplication:
8÷2 × 2 = 4 × 2 = 8
Substituting again:
3 − 45 + 8
Finally, we perform the subtraction:
3 - 45 = -42
Now we can substitute again:
-42 + 8
And perform the addition:
-42 + 8 = -34
Therefore, the simplified expression is -34.