Final answer:
To evaluate the expression (1+1)² [4-(4-1)²] using the order of operations, start by solving the expression inside the parentheses, then the second set of parentheses, and finally the remaining operations. The result is -20.
Step-by-step explanation:
To evaluate the exponential expression (1+1)² [4-(4-1)²], we need to follow the order of operations, which is also known as PEMDAS. To follow the order of operations and evaluate the exponential expression (1+1)² [4-(4-1)²], we start with parentheses, then exponents, followed by multiplication and division (from left to right), and then addition and subtraction (from left to right).
First, we solve the expression inside the parentheses: (1+1) equals 2. So now the expression becomes 2² [4-(4-1)²].
Next, we solve the expression inside the second set of parentheses: (4-1) equals 3. The expression now becomes 2² [4-3²].
Finally, we square the 3 and subtract it from 4: 4-3² equals 4-9 equals -5. The expression now becomes 2² [-5].
And finally, we square the 2: 2² equals 4. So the final result is 4 times -5, which is -20.