To simplify the expression 2(a^2 - ab) + 3 - ab, we need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).

Parentheses:
There are no parentheses in the given expression, so we can move on to the next step.

Exponents:
There are no exponents in the given expression, so we can move on to the next step.

Multiplication:
We have two terms to multiply: 2 and (a^2 - ab).

2 * (a^2 - ab) = 2a^2 - 2ab

Now the expression becomes: 2a^2 - 2ab + 3 - ab

Addition and Subtraction:
We have three terms to add/subtract: 2a^2, -2ab, and -ab.

Combining like terms, we get:
2a^2 - 2ab - ab + 3

Now let's simplify the expression further by combining the like terms:

2a^2 - 2ab - ab + 3 = 2a^2 - 3ab + 3

So, the simplified expression is 2a^2 - 3ab + 3.

Now, to find the value of the expression when a is equal to 2 and b is equal to -1, we substitute these values into the expression.

Replacing a with 2 and b with -1, we get:

2(2^2) - 3(2)(-1) + 3

Simplifying further:
2(4) + 6 + 3 = 8 + 6 + 3 = 17

Therefore, when a is equal to 2 and b is equal to -1, the value of the expression 2(a^2 - ab) + 3 - ab is 17.