Example: Evaluating expressions with 2 variables

We're asked to evaluate the expression a squared plus 10b minus 8 when a is equal to 7 and b is equal to 4. So to evaluate the expression, we really just have to substitute a with 7 and substitute b with negative 4 because they're saying evaluate it when a is equal to 7 and b is equal to negative 4. So let's do that. So a everywhere we see an a in the expression, we should put a 7 there. So instead of a squared, we should write 7 squared plus-- I'll do it in that same color-- plus 10 times b. But instead of a b there, we are now going to substitute it with b is equal to negative 4. So 10 times negative 4 instead of the b right over there. And then we have the minus 8. And now we just have to evaluate this thing. 7 squared is 49. And then 10 times negative 4. Remember, order of operations, multiplication comes before addition. So we have to multiply this. 10 times negative 4 is negative 40. So it's negative 40. And then we have minus 8 back over here. And so we get 49 plus negative 40, which is really the same thing as 49 minus 40 is going to be 9. And then we're going to subtract 8 from that. And so we get 1. 49 minus 40 is 9 minus 8 is 1. And we are done. We've evaluated the expression when a is equal to 7 and b is equal to negative 4.