How do you simplify #(63x + 6y) + (-16x + 46y) #?
"You'll have to count apples as apples and oranges as oranges."
In this case, the apples would be the x, and the oranges would be the y (or vice versa).
Well, in other words, you cannot add x and y together because they are two different things, so just leave them separate.
Anyway, it is just a matter of opening the parentheses and do simple additions.
Remember the rules:
Let's open all those parentheses without any worry of changing signs in this case.
Note: the MINUS sign here is associated to the number 16. It is really just (-16). The sign outside the parentheses are all +.
So, we have:
Now we have to count the x together and the y together.
We group them together (it's easier to see) and have:
Here, you see, we are gathering the apples (x) and the oranges (y) together.
You could factor out the x and y and rewrite this as follow:
if it makes you feel more comfortable doing the addition (subtraction).
so we have
which cannot be simplified further.
That's it. Hope it helped.