To evaluate the expression \(2 + 3 \times 16 - 2 \times 21 - 3\) using the order of operations (also known as PEMDAS/BODMAS), we first perform multiplication and then carry out addition and subtraction from left to right.
- Calculate the products:
- \(3 \times 16 = 48\)
- \(2 \times 21 = 42\)
So the expression becomes: \[ 2 + 48 - 42 - 3 \]
- Perform the addition and subtraction from left to right:
- \(2 + 48 = 50\)
- \(50 - 42 = 8\)
- \(8 - 3 = 5\)
Thus, the value of the expression is: \[ \boxed{5} \]