# Thread: Order of operations - parenthesis with 3 variables each

1. ## Order of operations - parenthesis with 3 variables each

I am trying to brush up on my algebra. I am getting a different answer than the back of the book. The numbers are the same but the order is different.

Write without parenthesis.

(a + b + 2) (c + d -3)

I get

ac + ad -3a + bc +bd - 3d + 2c +2d - 6

the back of the book shows

ac + bc + ad + bd -3a - 3b + 2c + 2d - 6

What is the correct order of distribution?

2. I don't know that there is a "correct" order for such an exercise.

And keep in mind that order doesn't matter for addition, so you only need to have the right terms; the order in which you list those terms shouldn't count against you, at least if you keep the constant terms at the end.

3. The book is right.

$\displaystyle (a+b+2)(c+d-3)$
=$\displaystyle ac+bc+2c+ad+bd+2d-3a-3b-6$
=$\displaystyle ac + bc + ad + bd -3a - 3b + 2c + 2d - 6$

4. Originally Posted by mathmonkey
...
Write without parenthesis
(a + b + 2) (c + d -3)

I get

ac + ad -3a + bc +bd - 3d + 2c +2d - 6

the back of the book shows
...

What is the correct order of distribution?
Which ever is most meaningful to you.
The procedure you use, is the one I find best.
I proceed from left to right.
After a is 'distributed', I strike it out.
Then b and then 2.