The *complete simple polynomial 3x2y2 − 2xy5* and the complex conjugate of it, the constant term of the polytope, are two of our most **important spatial structures**.

They form part of **many educational experiences**, from tracing a circle to constructing your own room in a house. In fact, **many people use** these two polynomials as stepping stones to more complex structures.

For example, tracing a circle is often followed by constructing a sphere or other shape. Once that is done, then you move on to creating another shape with that same space and structure.

You get the chance to test your skills again and again by changing what you use for structure and space.

## The x variables in each polynomial are the same

All the y variables are also the same length and −y2 + x + 2 = 0.

So, it doesn’t matter which polynomial you start with. You can add or subtrahenomials to get a new polynomial.

The only difference is what **letters appear** at the top of the polynomial to column index and bank of variables. Some **letters represent different commands** for adding or subtracting from or from zero, respectively.

Thus, when doing *fractions asymptote*, it matters which zero you use to add or subtract from the polynomial.

## The y variables in each polynomial are the same

All the other variables are different ones for each polynomial.

For example, the x and y variables for the second polynomial are not the same as the first one. The second one has a bigger value for x and a smaller value for y.

So, the complete sum of the *polynomials 3x2y2 − 2xy5* and −3x2y2 + 3x4y is not a number at all, but something much more beautiful.

There are many reasons to know about polynomials. First, it can be fun to write them in ways that have unexpected values. For example, if you wrote 3x2y2 + *2xy4 − 2xy5* + 5 as *5×5 − 12*, you would get a much nicer result than just writing 5!

## The constants of each polynomial are the same

The constants of the complete sum of the *polynomials 3x2y2 − 2xy5* and −3x2y2 + 3x4y are 2 and −1, respectively. These two constants determine how large each polynomial is in size.

Most people do not recognize the constant values of a polynomial, since they usually think of a smaller size polynomial when they hear the term “polynomial.”

A smaller polynomial may be harder to solve, which can cause frustration or even put you out of focus for another problem. When this happens, you **may need help** from someone else to solve it for you.

However, having a **small size polynomial might** not be what you want when it comes to wanting to know how fast that polynomial is evolving.

## True simplification of this sum is impossible using algebraic techniques

Using algebra to simplify the 3x2y2 − 2xy5 and −3x2y2 + 3x4y problems is a wasted trip.

Both of these problems have more than one variable, which makes them harder to solve. Also, both of these problems have complicated solutions, which makes you feel smarter if you can find the simpler one.

There are two ways to simplify these problems. The first is to **use consecutive solving techniques**. The second is *using simultaneous solving techniques*. Using consecutive solving techniques can help speed up your process, as it can help reach a stopping point. Using simultaneous solving techniques may allow you to get another solution as well.