I've been asked to make a video on algebraic division or algebraic long division.

But anyway, back to this algebraic long division.

You would just have to do the algebraic steps.

So I'll make a video an algebraic long division.

You don't have to when you do algebraic long division.

This is just an algebraic way of stating our problem.

Responsible for the computation of the algebraic equation of a locus.

Algebraic expressions and equations, and ending with a bit of graphing.

Let's actually do the algebraic multiplication and see what we get.

And now we just do a little bit of algebraic multiplication.

We set it up as an equation, so it is an algebraic representation.

It doesn't look like this is really an easy algebraic equation to solve.

And you know, you can do that without thinking in strict algebraic terms.

I'd like to challenge you to find an algebraic relationship between b and r.

But I'll show you the algebraic way, because when problems get complicated, this'll always work.

Welcome to the presentation on solving inequalities or I guess you could call them algebraic inequalities.

We set up the equation, we just have to use our algebraic tools to solve for 'B'

We live in a society that completely tends to valorize symbolic forms of representation algebraic representations, equations, codes.

We didn't define it in terms of an algebraic expression, we defined in terms of an actual visual graph.

Pi is a transcendental number, which means that it is not algebraic, never stops and doesn't have a pattern.

And there's an easier way of doing this kind of in your head, and this is the algebraic way that'll always work.

You might say, oh, my God, to multiply these using algebraic multiplication would take forever, then I'd have to factor it and simplify it.

We'll see that they would get much more nuanced and deep and frankly more beautiful as we start studying more and more algebraic ideas.

In the next few videos, we'll see more algebraic ways of solving these than drawing their two graphs and trying to find their intersection points.

And that you just don't view this as some kind of mechanical way to get problems right on a test that only tests algebraic long division.

When you construct a locus, you can click on it with the right mouse button and select cartesian equation to see its cartesian equation, whenever it is an algebraic curve of low degree.

An affine algebraic group over a field k is a representable covariant functor from the category of commutative algebras over k to the category of groups such that the representing algebra is finitely generated.

Well, anyway, the next step if we really want to decompose this rational expression is to figure out what this part of it is, and the way to do that is with algebraic long division.

So the first step we want to do to simplify this and to get it to the point where the numerator has a lower degree than the denominator is to do a little bit of algebraic division.

So if we were to divide both sides of this by r squared, we would get and this is just little algebraic manipulation x squared over r squared plus y squared over r squared is equal to 1.

But what we want to propose, is that the highest levels of abstraction, things like mathematics, computing, logic, etc. all of this can be engaged with, not just through purely cerebral algebraic symbolic methods, but by literally, physically playing with ideas.

They are moving in the same general direction, in fact the exact same general direction, if we are looking at it from an algebraic point of view, we would say they have the same slope, but they have different intersect, they involve different points.

So I'll show you I showed you that 1, you could define a function as just kind of a standard algebraic expression, you could also do it a kind of if number is odd, this is what you do, if a number is this, is what you do.

In our minds, it's much more valuable to have a deep understanding of algebra, and to be able to see the world in algebraic way, then to just get through algebra and to just kind of understand calculus, without being able to apply or really fundamentally understand either .

The first thing to do with any of these rational expressions that you want to decompose is to just make sure that the numerator is of a lower degree than the denominator, and if it's not, then you just do the algebraic long division like we did in the first video.