# Thread: Simplifying - combining like terms

1. ## Simplifying - combining like terms

Expression to be simplified: -9y + 2 - 4y - 8x + 12 - x

Step 1: Change values
-9y + 2 - 4y - 8x + 12 - x = -9y + 2 + (-4y) + (-8x) + 12 + (-1x)
Step 2: Apply commutative property
= -9y + (-4y) + 2 + 12 + (-8x) + (-1x)
Step 3: Combine like terms
= (-9 + [-4])y + 2 + 12 + (-8 + [-1])x
Step 4: Simplify
= -13y + 14 + (-9x)

Should this actually be written as -13y + 14 - 9x? Should terms without variables be added after those with variables? Do these things matter? The books gives an answer of -13y - 9x + 14.

2. Originally Posted by Euclid Alexandria
Expression to be simplified: -9y + 2 - 4y - 8x + 12 - x

Step 1: Change values
-9y + 2 - 4y - 8x + 12 - x = -9y + 2 + (-4y) + (-8x) + 12 + (-1x)
Step 2: Apply commutative property
= -9y + (-4y) + 2 + 12 + (-8x) + (-1x)
Step 3: Combine like terms
= (-9 + [-4])y + 2 + 12 + (-8 + [-1])x
Step 4: Simplify
= -13y + 14 + (-9x)

Should this actually be written as -13y + 14 - 9x? Should terms without variables be added after those with variables? Do these things matter? The books gives an answer of -13y - 9x + 14.
Because addition is associative, it doesn't really matter what order the terms appear. However, standard practice says to list terms with variables first, so the book is technically "more correct." The irony here is that when listing the variable terms first, the standard is to list them in alphabetical order, so the "best" answer is -9x-13y+14. So the book isn't quite right, either. However, the whole ordering thing is splitting hairs as all of the answers say exactly the same thing.

-Dan

3. Thanks for the feedback. I think textbooks would be doing noobs a big favor to list all possible answers the first few times material like this is covered. After that, I think people would get the point, but it's confusing at first. Maybe I should write a letter (like I have the time though!).