meshackb wrote:

Ok, I think I get it... jeez, all these finer points of math that they never taught in high school are killing me. I knew I had to do factoring somewhere in this problem, but I was stuck on thinking I couldn't rearrange the terms.

So if I understand, this is what you are saying.

In this problem we basically have

a + b - c + d =

as long as we keep (b - c), we can rearrange the other terms around that however we like correct?

So the next step is basically

a + d + b - c = { b-c still in same order }

But to do this would be illegal, correct?:

a - c + d + b =

No, you are looking at it incorrectly. You can rearrange terms in an equation as long as you keep the 'signs' before the terms.

Example, if you are given a+b-c+d , then you can also write it as a+d+b-c or a+d-c+b or -c+b+d+a as long as you keep + sign in front of a,b and d and - sign before c.

Finally any number 'a' is actually +a as 'a'= 0+a.

This is all you need to remember for rearranging the terms. You can rearrange all you want but make sure to keep the signs intact.

Side note, a- c + d + b is completely legal as you are still maintaining the correct signs before the variables. It does not matter if you write a+b-c+d or -c+a+b+d or d-c+a+b as we are still maintaining the signs. Another way to look at it is this: If we write b-c, we can also write it as : b+(-c). This does not violate any rule.

Now, as I stated above that a+b = b+a, thus b-c = b+(-c)= -c+b

Hope this helps.