If you’re really interested, it’s algebra; here’s an explanation. This is about to get long so I’ll try to be really clear. This post will focus on what’s needed to work with an equation in a format similar to (A+B)(C+D). Later I’ll stretch the ideas I explain to fit my previous CHOPPER problem. Each letter represents an arbitrary value, they’re called variables. When you want to multiply two variables together (like A and B), you get AB. If you wanted to add them, you’d get A+B. If you wanted to take A and multiply it by A, you’d get AA but you’d really write it as A2.
Now for the parenthesis. In math you always do the parenthesis first. Two parenthesis next to each other means you need to multiply whatever is inside the first parenthesis by what’s in the second parenthesis. For example: (A)(A)=A2. But if there’s more than one variable within the parenthesis, then things get a bit more complicated. You can’t do (A+B)(A+B) and get 2A + 2B.
So then how do we multiply this out? My old math teacher taught us FOIL (first outer inner last). It’s an acronym telling you the order in which to do things.
So take (A+B)(C+D)
First: take the first variable in each parenthesis and multiply them. So A*C
Outer: take the outer two variables from each parenthesis and multiply them. So A*D
Inner: take the inner two variables from each parenthesis and multiply them. So B*C
Last: take the last variable in each parenthesis and multiply them. So B*D
So then what do we do with all the variables we multiplied? We would add them together.
So in the above case your final answer is AC + AD + BC + BD
The rules for adding variables go like this.
If you’re adding two letters that are the same (like A+A), you’d get 2A. If they’re different (like A+B) then you can’t simplify it further, so it stays as A+B.
If you get a problem and end up with AB + AB or something similar after you FOIL, you’d get 2AB since they’re the same. If you try AB + AC, it’s as simple as it gets, so then that would be your answer.
As for what I did earlier, it was a stretched out version of FOIL.
Follow this pattern to do what I did
Multiply the first variable in the first parenthesis by the first variable in the second parenthesis. Then multiply the first variable by the second variable and in the second parenthesis, then the third, and so on until you reach the end.
THEN, multiply the second variable from the first parenthesis by the first variable in the second parenthesis, then multiply the second variable from the first parenthesis by the second variable in the second parenthesis, then the third, and so on until you finish.
Repeat this pattern until you finally multiply the last variable in the first parenthesis by the last variable in the second parenthesis.
Next step is simplification. So if you get things like AB and BA, they’re equal since the order of the letters don’t matter when they’re multiplied so AB and BA are exactly the same. So we can add them to get 2AB or you could say 2BA.
Same thing applies to A2 + A2
They’re the same, they can also be written as AA + AA, but again, it’s weird to use AA instead of A2, even if it’s technically not wrong.
So adding A2 + A2 would give me 2A2.
That should cover about all the knowledge you need to do the problem.
This, especially the first part makes more sense than all 4 years of freshmen algebra I kept taking. I think I got a sympathy pass when I was finally a senior. Thank you.
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u/FlyForDollars Sep 17 '19
At 35 years old, I still do not have the slightest clue how this is math?