Evaluating expressions with & without parentheses

what I want to do is think about whether this expression right over here would evaluate the same way whether or not we had parentheses so to think about that let's first think about how it would evaluate if we have the parentheses so if we add the parentheses we want to do whatever in the parentheses first and so here we have 8 minus 3 which is equal to 5 so this simplifies to 5 times 5 times 8 minus 3 and now we want to do the multiplication before we do subtraction this goes back to order of operations you do your multiplication and division first well you do your parentheses first then if you have multiplication division and addition and subtraction all in a row you want to do your multiplication and your division first so here we're going to multiply 5 times 8 to get 40 and then we're going to subtract 3 to get 37 now let's think about what this will do it about this what this would evaluate to if we did not have the parentheses so it would be 8 minus 3 times 8 minus 3 so we just have to remind ourselves about the order of operations the convention is is to do your multiplication first so you're actually going to multiply the 3 times the 8 before you subtract it from this 8 and then before you subtract this 3 so we took away the parentheses but the order of operations say hey do this multiplication first we could even put a parenthesis here to emphasize that so this will become 8 minus 8 minus 24 so let me write this way 8 minus 24 minus 3 8 minus 24 minus 3 now 8 minus 24 is negative 16 you subtract a negative another 3 you're going to get 2 negative 19 so clearly clearly you get very very different values depending on whether or not you have parentheses