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.