Ok, I admit it: I'm an idiot when it comes to intermediate or advanced mathematics. (Solving for X was the extent of my mathematical abilities until recently, and it's still not too far from the top of my list, now.)
I'm working through a textbook and I've come across a problem whose answer I just can't seem to get. I've had a breeze of things so far, so this one is bugging the living crap out of me, and I'd appreciate some help.
Ok, I'm suppose to calculate and simplify the following polynomial:
(2x^2y-3xy^3)(xy+7y^3)
The given answer is
2x^3y^2+11x^2y^4-21xy^6
What I don't get is the 11x^2y^4 part....
I understand how to get the first and last terms ( 2x^3y^2 & 21xy^6 ), but that one in the middle is eluding me. Can anyone help?
And when the hell are they going to incorporate LaTex here? I HATE typing ^n for every damn exponent!
I now indipedently try do it in real time.
(2x^2y-3xy^3)(xy+7y^3)=2x^3y^2+14x^2y^4-3x^2y^4-21xy^6. Easy
Now I see that maybe need somthing minus
so
2x^3y^2+14x^2y^4-3x^2y^4-21xy^6=2x^3y^2+11x^2y^4-21xy^6.
You can't do this 14x^2y^4-3x^2y^4=11x^2y^4 ?
(2x^2y-3xy^3)(xy+7y^3)=2x^3y^2+14x^2y^4-3x^2y^4-21xy^6. Easy
Now I see that maybe need somthing minus
so
2x^3y^2+14x^2y^4-3x^2y^4-21xy^6=2x^3y^2+11x^2y^4-21xy^6.
You can't do this 14x^2y^4-3x^2y^4=11x^2y^4 ?
A polynomial can always be written as a sum of monomials, and a monomial can always be written as a number times a product of powers of variable terms where no variable happens twice, and the variables are in lexicographic order (dictionary order). But two monomials with exactly the same variable content where the variables are raised to exactly the same power can be added....
QUOTE (BigDumbWeirdo+Mar 27 2008, 04:17 PM)
(2x^2y-3xy^3)(xy+7y^3)
= [ 2 (x^2y^1) + -3 (x^1y^3) ] [ 1 (x^1y^1) + 7 (x^0y^3) ] { Write out all four terms in long hand -- treat the variable as if they were primitive terms for now. }
= (2)(1)(x^2y^1)(x^1y^1) + (2)(7)(x^2y^1)(x^0y^3) + (-3)(1)(x^1y^3)(x^1y^1) + (-3)(7)(x^1y^3)(x^0y^3) {Use the distributive law twice to write out the four unsimplified monomials. }
= 2 (x^3y^2) + 14 (x^2y^4) + -3 (x^2y^4) + -21 (x^1y^6) {Now use the arithmetic and exponent rules to simplify the monomials. Here we see that two monomials have the same variables raised to the same exponent. That means ...}
= 2 (x^3y^2) + (14 + -3) (x^2y^4) + -21 (x^1y^6) { ... we can use the distributive property in reverse.}
= 2 x^3y^2 + 11 x^2y^4 - 21 xy^6 { More arithmetic. }
= [ 2 (x^2y^1) + -3 (x^1y^3) ] [ 1 (x^1y^1) + 7 (x^0y^3) ] { Write out all four terms in long hand -- treat the variable as if they were primitive terms for now. }
= (2)(1)(x^2y^1)(x^1y^1) + (2)(7)(x^2y^1)(x^0y^3) + (-3)(1)(x^1y^3)(x^1y^1) + (-3)(7)(x^1y^3)(x^0y^3) {Use the distributive law twice to write out the four unsimplified monomials. }
= 2 (x^3y^2) + 14 (x^2y^4) + -3 (x^2y^4) + -21 (x^1y^6) {Now use the arithmetic and exponent rules to simplify the monomials. Here we see that two monomials have the same variables raised to the same exponent. That means ...}
= 2 (x^3y^2) + (14 + -3) (x^2y^4) + -21 (x^1y^6) { ... we can use the distributive property in reverse.}
= 2 x^3y^2 + 11 x^2y^4 - 21 xy^6 { More arithmetic. }
QUOTE (BigDumbWeirdo+Mar 27 2008, 04:17 PM)
2x^3y^2+11x^2y^4-21xy^6
What I don't get is the 11x^2y^4 part....
What I don't get is the 11x^2y^4 part....
QUOTE (BigDumbWeirdo+Mar 27 2008, 04:17 PM)
And when the hell are they going to incorporate LaTex here? I HATE typing ^n for every damn exponent!
But then you'ld be writing ^{n} :-)
QUOTE (DavidD+Mar 27 2008, 05:01 PM)
I now indipedently try do it in real time.
(2x^2y-3xy^3)(xy+7y^3)=2x^3y^2+14x^2y^4-3x^2y^4-21xy^6. Easy
Now I see that maybe need somthing minus
so
2x^3y^2+14x^2y^4-3x^2y^4-21xy^6=2x^3y^2+11x^2y^4-21xy^6.
You can't do this 14x^2y^4-3x^2y^4=11x^2y^4 ?
Please try to keep your gibberish out of the Homework Help section.
(2x^2y-3xy^3)(xy+7y^3)=2x^3y^2+14x^2y^4-3x^2y^4-21xy^6. Easy
Now I see that maybe need somthing minus
so
2x^3y^2+14x^2y^4-3x^2y^4-21xy^6=2x^3y^2+11x^2y^4-21xy^6.
You can't do this 14x^2y^4-3x^2y^4=11x^2y^4 ?
Please try to keep your gibberish out of the Homework Help section.
QUOTE (DavidD+Mar 27 2008, 12:01 PM)
I now indipedently try do it in real time...
Uhhhh... Is that suppose to answer my question?
Uhhhh... Is that suppose to answer my question?
QUOTE (rpenner+)
A polynomial can always be written as a sum of monomials, and a monomial can always be written as a number times a product of powers of variable terms where no variable happens twice, and the variables are in lexicographic order (dictionary order). But two monomials with exactly the same variable content where the variables are raised to exactly the same power can be added....
Thanks. That actually explained it to me
I don't really care what I have to type, only the way it shows up. It looks like the terms in the first polynomial are 2x, 2y, -3xy & 3, this way. I haven't screwed up yet from reading exponents this way, but I know I will. It's only a matter of time...
Damnit, Sapo's Joint has LaTex!
I don't really care what I have to type, only the way it shows up. It looks like the terms in the first polynomial are 2x, 2y, -3xy & 3, this way. I haven't screwed up yet from reading exponents this way, but I know I will. It's only a matter of time...
Damnit, Sapo's Joint has LaTex!
Please try to keep your gibberish out of the Homework Help section.
Oddly enough, it seems as if he knew how to do it, and was just trying to be helpful, but his posts still look like they were translated by a computer from cyrillic to french, and then into english.
Thanks. That actually explained it to me
QUOTE
But then you'ld be writing ^{n} :-)
I don't really care what I have to type, only the way it shows up. It looks like the terms in the first polynomial are 2x, 2y, -3xy & 3, this way. I haven't screwed up yet from reading exponents this way, but I know I will. It's only a matter of time...
Damnit, Sapo's Joint has LaTex!
QUOTE (->
| QUOTE |
| But then you'ld be writing ^{n} :-) |
I don't really care what I have to type, only the way it shows up. It looks like the terms in the first polynomial are 2x, 2y, -3xy & 3, this way. I haven't screwed up yet from reading exponents this way, but I know I will. It's only a matter of time...
Damnit, Sapo's Joint has LaTex!
Please try to keep your gibberish out of the Homework Help section.
Oddly enough, it seems as if he knew how to do it, and was just trying to be helpful, but his posts still look like they were translated by a computer from cyrillic to french, and then into english.
QUOTE (DavidD+)
Oddly enough, it seems as if he knew how to do it, and was just trying to be helpful
DavidD helpful?
Edit: DavidD just gave me a negative
DavidD helpful?
Edit: DavidD just gave me a negative
QUOTE (TheDoc+Mar 27 2008, 12:30 PM)
DavidD helpful?
I said "trying to be helpful."
I said "trying to be helpful."
QUOTE (BigDumbWeirdo+Mar 27 2008, 05:48 PM)
I said "trying to be helpful."
Oh, I see the difference now
Oh, I see the difference now
Quote: David "Please get neg" ???
If you're going to neg someone (especially undeservedly) try to be more specific than "ugh".
If you're going to neg someone (especially undeservedly) try to be more specific than "ugh".
QUOTE (BigDumbWeirdo+Mar 27 2008, 05:22 PM)
Uhhhh... Is that suppose to answer my question?
I think you more smarter than I think...
edit: Nevermine, simple questions need leave for simple guys like TheDog.
I think you more smarter than I think...
edit: Nevermine, simple questions need leave for simple guys like TheDog.
QUOTE (DavidD+Mar 27 2008, 03:33 PM)
I think you more smarter than I think...
I think so, too
I think so, too
QUOTE (DavidD+Mar 27 2008, 08:33 PM)
I think you more smarter than I think...
edit: Nevermine, simple questions need leave for simple guys like TheDog.
Dude,
I thought you may be coming around, and then you edit an insult to one of my favorite guys here. Stick to your instincts. Have a normal conversation and bury that second personality so deep that you can't hear him anymore!
Peace and Serenity (Great movie, Great ship!),
Ron
edit: Nevermine, simple questions need leave for simple guys like TheDog.
Dude,
I thought you may be coming around, and then you edit an insult to one of my favorite guys here. Stick to your instincts. Have a normal conversation and bury that second personality so deep that you can't hear him anymore!
Peace and Serenity (Great movie, Great ship!),
Ron
QUOTE (BigDumbWeirdo+Mar 27 2008, 12:22 PM)
It's only a matter of time...
Damnit, Sapo's Joint has LaTex!
Thank you BDW!
Yes, but I have no idiots...
Actually, I have Mimetex right now. Almost the same, but not extensible via \usepackage statements.
I may leave the Mimetex in place for \picture elements, and use a different BBcode for chemical equations and other things. LaTeX output is much prettier than the cgi.
Trippy's request for the chemtex macros sent me down a frustrating road that leads me to think I bit off a lot in trying to implement LaTeX seamlessly.
Physorg's admins may have just given up on it, but I will not. I can't spend too much time at it right now, but it'll happen.
Damnit, Sapo's Joint has LaTex!
Thank you BDW!Yes, but I have no idiots...
Actually, I have Mimetex right now. Almost the same, but not extensible via \usepackage statements.
I may leave the Mimetex in place for \picture elements, and use a different BBcode for chemical equations and other things. LaTeX output is much prettier than the cgi.
Trippy's request for the chemtex macros sent me down a frustrating road that leads me to think I bit off a lot in trying to implement LaTeX seamlessly.
Physorg's admins may have just given up on it, but I will not. I can't spend too much time at it right now, but it'll happen.
QUOTE (DavidD+)
Nevermine, simple questions need leave for simple guys like TheDog.
Dogs are noble, friendly and loyal creatures. Thank you, David
Dogs are noble, friendly and loyal creatures. Thank you, David
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