akicilj, algebra division

[truepenny]

So if you have an algebra problem that looks like this:

(x + 2)(3x + 5) = 19

and you make it look like this:

3x² + 11x + 10 = 19

What is this process called?

(Yes, this is a question for The Mirador.)

(No, really.)

Comments

[kate_nepveu]

Multiplying polynomials?

Ambition, Distraction, Uglification, and Derision

[slithytove.livejournal.com]

"And what mean all these mysteries to me
Whose life is full of indices and surds?
x^2 + 7x + 53
= 11/3."

Sorry.

[wistling.livejournal.com]

Expansion.

http://en.wikipedia.org/wiki/Factorization

[fidelioscabinet.livejournal.com]

Lordamercy, child, what are those boys of yours getting up to?!

[xjenavivex.livejournal.com]

http://webpages.charter.net/thejacowskis/chapter6/section3.html

i agree it is multiplying polynomials

[magicnoire.livejournal.com]

Polynomial expansion.

[floatingtide.livejournal.com]

algebra-cadabra!

(Sorry. Not helpful).

[vass]

Do you mean what is it called in our world, or in Mélusine?

[torrilin.livejournal.com]

Going from 3x^2 + 11x + 10 = 19 to (x + 2)(3x + 5) = 19 is polynomial expansion. Going in the other direction is multiplying polynomials. I'm not sure why they'd *want* to go in the other direction tho, since if you're interested in actually working the equation, the expanded form is more useful. Either way, it is Useful Math.

[marinarusalka.livejournal.com]

Well, in this particular case, you would want to go the other way, so that you could turn it into 3x^2+11x-9=0 and use the quadratic formula. I don't think there's an easy way to solve the expanded form in this instance.

umn...

[anach.livejournal.com]

going from 3x^2 + 11x + 10 = 19 to (x+2)(3x+5) = 19 would be normally be called factoring the polynomial. Going the other route would be polynomial expansion or polynomial multiplication (or repeated use of the Distributive Property of Multiplication over Addition).

[sam-t.livejournal.com]

I think I'd call it 'multiplying out', but it's been a while since I've needed to call it anything.

[kaigou.livejournal.com]

My calculus prof just called it "reducing" -- that is, you're reducing the compacted version to its parts. Err, I think that was the logic. Expanded, reduced, pick one of the folks above, I suppose!

[fiamaya.livejournal.com]

I'd just call going from (x + 2)(3x + 5) to 3x^2 + 11x + 10 multiplying polynomials; people occasionally refer to the FOIL method (see here (http://www.purplemath.com/modules/polymult2.htm), but I'd be shocked to hear anyone other than a student or teaching in an algebra class call it that (ie, no one who works with polynomials professionally would use the term). It could be called "polynomial expansion", though I'd expect to hear that more for something like (4x+5)^10 -- something too annoying to multiply out.

Going the other way, from 3x^2 + 11x + 10 to (x + 2)(3x + 5), is called "factoring".

(I've got a math PhD, just for the credential. And would be happy to answer in more detail if you want.)

[malinaldarose.livejournal.com]

A headache.

Me = So not the math genius.

[jerusha.livejournal.com]

*laughs at/with your icon*

[malinaldarose.livejournal.com]

I love it -- the joke always makes me laugh.

[sleary.livejournal.com]

I've reformatted the algebra neurons; sorry. However, your comment reminded me to go put The Mirador on my wishlist -- more of a giant shopping cart organizer, really -- and hey! they seem to have some cover art!

(mmm, crypts.)

[pabba.livejournal.com]

Powers.

Sorry, I'm no help. But looks like several others found some good answers!

[miladyinsanity.livejournal.com]

Quadratic expansion. It's only got a power of 2 term. If it's more, you call it polynomial, sez she who's still studying this sort of thing. They are fun.

[eiriene.livejournal.com]

In common "math teacher" terms, it's referred to as "foiling".

[larryhammer]

Informally, multiplying out; more formally, multiplying polynomials.

The reverse process is factorization, the more common action.

---L.

[fiction-theory.livejournal.com]

They call it algebra, I call it a terrible thing to do to parantheses. Also, the reason I'm a writer and not a rocket scientist.

And even stupider remark - that's also called a parabola. Set it equalled to y, graph that sucker on a TI-83 and you basically get an arch. Yay parabolas, I guess.

So, the Mirador uses the Cartesian coordinate system? Huh. Interesting.

[mallory-blog.livejournal.com]

you foiled it

[amayaxellia.livejournal.com]

Bloody Hell *shriek*
Why would you want that ghastly stuff in The Mirador??
Well, in agreement with what they said above, Foiling, or polynomial expansion. o_O *remembers algebra homework*

[lareinenoire.livejournal.com]

I'm pretty sure it's called factoring equations. I do remember it involves the PEMDAS system. Ah, high school pre-calculus, how faintly I remember thee.

[(Anonymous)]

It's called expanding the equation (and moving it back into brackets is factorising it), or so I was taught. For reference, I'm British, dunno if Americans or whoever call it something else.

[(Anonymous)]

What about simplification? You're simplifying the equation. If that doesn't work for you, your best bet is probably polynomial expansion. I learned it as 'FOILing, but I don't know if you're looking for junior high math terms...

[(Anonymous)]

Distribution or simplifying