I’m having problems understanding algebra, specifically, the reasons behind simplifying monomials/polynomials. I feel like all I am doing is memorizing HOW and not WHY. All the material I have seen (including teachers) does not explain why we use the rules. For me this is important because up to this point I really don’t have to remember why I , for example, go backwards on the number line. Or why multiplying a number by it’s decimal point provides the percentage. When it comes to simplifying algebriac fractions I have very little visual reference for figuring out the problems.
Are there some common visual concepts that can help give visual direct to why the rules of solving algebra or am I stuck doing the problems a certain way because “that’s what they tell you to do” ?
short answer is : the same reason you learned multiplication tables. it makes life easier for you in the future so just trust us and learn it.
a slightly longer answer: "it's required for engineering / math" you need to be able to freely the manipulate expressions into the required form so you can do something useful with it.
half the engineering faggots who fail out of signal processing 101 or electromagnetic fields 101 do so because they suck balls at algebra and can't correctly get the formula into the necessary format to apply their domain transforms.
those same faggots would get triple fucked in any 400+ math course where proving patterns in results sometimes requires some very creative manipulation.
David Thompson
i was assuming you were asking "why do we learn this shit"
if you're asking "why do these techniques work?" then please post a more specific question
Hunter Thompson
Thanks user, this inspired me.
>"why do these techniques work?" then please post a more specific question
Here's one: Why do we negative numbers cancel when square?
why does -4^2 = 256 and not -256?
Tyler Reyes
Well considering -4^2 = 16 you tell me.
Parker Carter
whoops ...
>KS
Nolan Martin
Its so weird seeing that picture because I was there when it was taken
Blake Mitchell
What happens you multiply a negative number by another negative number? I know that doesn't fully answer your question but it gives you something to google now. There are a lot of videos on the proof. The don't teach it in introductory algebra because it is not necessary or the reason you learn introductory algebra, and would unnecessarily complicate the course. Focus on techniques
Noah Reyes
It's more useful the higher up you go in math.
You'll use simplification immediately as you enter Calculus, for example, when trying to evaluate a limit. You could plug in numbers at any time along the way to see what's happening, but usually you have to simplify it quite a ways down to get the "real" answer instead of a "fake" one (that is still technically correct).
Of course, you could also just cheat and use a calculator/solver/etc, but since you can't do that with everything in the future you might as well at least know how to do it.
Christopher Walker
Because math is an entirely human invention, so the rules are sometimes arbitrary. That's why.
Ian Campbell
>hurr durr negative-negative multiplication is axiomatic No its not you fucking brainlet
Your question is really "what does it mean to multiply by a negative number?" Also keep in mind that multiplication is commutative
Joshua King
Wow, what a helpful and informative response. You sure showed me.
Evan King
First..... 4^2=16, not 256.... Maybe you where thinking 4^4?
Here's the best explanation for this particular question.
when you multiply a base you add the exponents.
(a^n)(a^m)=a^(n+m)
What you're missing is the fact that we simply don't usually express numbers when they have a power of 1 or 0.
So -4^2 is the same as (-4^1)(-4^1), if you have -4^3 then we can use either (-4^1)(-4^1)(-4^1) or if we need to we can do (-4^2)(-4^1).
I'll even go on to mention that even when you have a polynomial function such as f(x)= 3x^2+5x-7 we are ignoring/assuming that it is the same as 3x^2+5x^1-7x^0 which is important later in calculus.
Brody Ross
Not the same guy but you are either a troll or uneducated. If you're a troll it then fuck you, you don't deserve a "helpful" or "informative" response.
Or you are so uneducated and lack the proper understandings and fundamentals of mathematics to allow yourself to believe such a statement that the amount of education and "proof" to enlighten, educate, and "change your mind" would be equivalent to tens of thousands of dollars in university education along with a couple thousand hours of personal learning and studying. This will not be conveyed through Veeky Forums and in all honesty if you truly sought education you can get a googling, buy some textbooks, and get reading.
Just because you make a cunt of a statement does not entitle you to an answer or make someone calling you out for being an uneducated cunt "unhelpful".
So fuck right off.
Andrew Garcia
We sometimes choose foundations in a way to let us prove shit we like by convention. Hell, some times we even put it as an axiom like the fact that 0 doesn't has an inverse. We state it as that in the field of real numbers because we would get prove any number is equal to any other number. With multiplication, it's not taken axiomatically, but it's derived from other properties we choose to grab from the real numbers, the key one being the uniqueness of aditive inverses in the reals. It's not axiomatic, but it has been taken as such in the past and most of the justification came from the double negation in logic which isn't a proof. Its was taken as such because it facilitaded techniques in arithmetic. To be pedantic, without talking about modern foundations, you have to assume that (-1)a=-a to get to a contradiction.
Carter Lewis
If you are asking specific questions I am certain that me or someone else can answer them.
Most of the time you can figure out why things are the way they are by looking for a contradiction.
Look at the problem of (-4)^2.
(-4)^2=(-4)*(-4)
Now assume that the answer is -16.
Then we have (-4)*(-4)=-16
Which is false because -16 is also 4*(-4).
So we have
(-4)*(-4)=(-4)*4
Now divide both sides by (-4) and you have
(-4)=4
Which seems clearly wrong.
Xavier Scott
Great example of proof by contradiction.
Sebastian Cox
This is from Euler is this similarly like a proof by contradiction?
Joshua Young
same grill?
John Stewart
Yes it is very similar. Euler is doing essentially the same, but more general and a bit shorter.
>best explanation >presupposes homomorphicity of the exponential function and knowledge of polynomials in order to explain basic properties of multiplication
OP, here's an example from Electrical Engineering (might not be what YOU are doing, but it is a reason why they teach everyone to simplify polynomials... so the ones who want to engineer already have the skills). Anyway, when trying to find the output voltage of a current through a circuit (a filter that gets rid of DC voltage, for example (LP Filter for EngAnons)). you can model the circuit elements into one equation, which will most likely have a 2nd order polynomial in the denominator. You can easily find the frequencies that the filter will cut-off by simplifying this polynomial down.
Christopher King
Fucking lol
Nicholas Taylor
Imagine negative means opposite of, so when you times -4 by -4 it's like saying the opposite amount of 4 times the opposite amount of 4 or -(4(-4)). So a negative*negative is like saying the opposite of the opposite which is just the original thing like the opposite of the opposite of hot is hot because the opposite of hot is cold and its opposite is hot which is the first thing you started with
