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

1 Answer
Sep 20, 2015

#47x + 52y#


"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).

#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.