Question

How do you simplify `(63x + 6y) + (-16x + 46y)`?

Answer 1

`47x + 52y`

Explanation:

"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:
`(a+b) =a+b`
`-(a+b) = -a - b`
`-(a-b) = -a +b`

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:
`(63x + 6y) + (- 16x + 46y)`
`= 63x + 6y - 16x + 46y`

Now we have to count the x together and the y together.
We group them together (it's easier to see) and have:
`= 63x-16x + 6y+46y`
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:
`= (63-16)x + (6+46)y`
if it makes you feel more comfortable doing the addition (subtraction).

Finally,
`63-16 = 47` and
`6+46 = 52`
so we have
`(63x + 6y) + (- 16x + 46y) = 47x + 52y`

which cannot be simplified further.

That's it. Hope it helped.