Subtracting polynomials is an operation that is performed with algebraic expressions.
A polynomial is an algebraic expression formed by joining two or more constants and variables, related through subtraction, addition or multiplication operations. Different calculations can be carried out with polynomials.
To perform a subtraction of polynomials , it is necessary to group the monomials (the expressions of a single term) according to their characteristics and proceed to simplify those that are similar. The operation itself is performed by adding the opposite of the subtrahend to the minuend .
Polynomial Subtraction Example
Let's take the following example: P(x) − Q(x) = (4×3 + 2x − 5) − (3×3 − 4×2 + 5x)
As explained above, we have to modify the signs of the subtrahend to perform the operation: 4×3 + 2x − 5 − 3×3 + 4×2 − 5x . As you can see, the signs of the minuend do not change (4×3 + 2x − 5) .
Once this is done, we must group and simplify the monomials: 4×3 − 3×3 + 4×2 + 2x − 5x − 5 .
Finally we complete the operation according to the remaining monomials: x3 + 4×2 − 3x − 5 .
The result of the subtraction of polynomials (4×3 + 2x − 5) − (3×3 − 4×2 + 5x) is, ultimately, x3 + 4×2 − 3x − 5 .
To develop a subtraction of polynomials, different techniques can be applied.
Different techniques
Another way to subtract polynomials is to write the opposite of each one below the other . Thus, the similar monomials will remain in columns and we can proceed to add them.
It is important to keep in mind that it does not matter which of the polynomial subtraction techniques we choose: the result of the operation, as long as it is performed correctly, will be the same.
Application of subtraction of polynomials and other operations
Polynomials have various applications outside the field of mathematics and, in the same way as with many other concepts that are too specific at first glance, we are not always aware of it. One of the cases in which they are of great help is the alignment of electromagnetic antennas, something that many people do daily when installing wireless Internet networks (Wi-Fi).
To design a 2.4 GHz antenna capable of connecting equipment to a Wi-Fi network, it is necessary to use Chebyshev polynomials , which allow the current to be appropriately distributed in each element of the array and to find the appropriate physical dimensions based on said data. The Chebyshev polynomials were named in honor of the Russian mathematician Pafnuti Chebyshev, and it is a family that can be easily defined recursively, the same thing that happens with the Fibonacci numbers, for example.
Another application of polynomials is in biology, since it is possible to calculate the population of a bacterial culture through polynomial expansions . In mathematics, the expansion of a product of sums means a sum of products (multiplication is distributive with respect to addition); In the case of polynomials, this can be obtained by repeatedly replacing subexpressions that multiply two others (at least one of which must be a sum) by the equivalent sum of products, and so on until the entire expression becomes a sum of products.
Calculations performed in biology
Also within biology, polynomials are used to calculate the three-dimensional structure of proteins (x-ray crystallography) and to know how much a disease has spread from the contact that has taken place between a group of people. infected and another of healthy people. Statistics also takes advantage of them, in fact more than other fields; for example, to estimate a company's potential sales over the next fiscal year, or to forecast the weather taking into account variables such as temperature, air masses and pressure.
As can be seen, the subtraction of polynomials is a simple procedure compared to others that also involve this type of algebraic expressions, but that does not mean that it is not present as part of some of them.