Addition, subtraction and multiplication of polynomials

In this video I will explain how do operations with polynomials but above all we will focus on the multiplication of polynomials.

In mathematics, a polynomial is a mathematical expression made up of a finite set of variables (not determined or unknown) and constants (fixed numbers called coefficients), using only the arithmetic operations of addition, subtraction and multiplication, as well as integer exponents positive.

The operations with polynomials are done as follows:

• sum of polynomials: To add polynomials we will add the coefficients of the terms of the same degree (we will leave the rest the same). Polynomials can be added and subtracted by grouping the terms together and simplifying like monomials.
• subtraction of polynomials: To subtract polynomials, we will add the opposite of the subtrahend to the minuend, that is, we will change the sign of all the monomials in the subtrahend in order to carry out a sum of polynomials.
• multiplication of polynomials1: we will carry out a normal multiplication but with polynomials. To multiply polynomials, each term of a polynomial is multiplied by each one of the terms of the other polynomial and then similar monomials are simplified.
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• multiplication of polynomials 2:We will multiply each of the terms or monomials of a polynomial by each of the terms of the other. Afterwards, the terms of the same degree will be added and the others will be left the same.

To say in another way that it is a polynomial, we could say that it is an n-ary relation of monomials, or a succession of additions and subtractions of integer powers of one or several indeterminate variables.

Adding polynomials involves combining terms. Like terms are monomials that contain the same variable or variables raised to the same power. The following are examples of like and dissimilar terms:

All these operations with polynomials You will understand them much better with the video and you can also practice them with our printable exercises with their solutions.

The division or quotient of polynomials We will see it in the next video.

If you want to read more articles similar to Addition, subtraction and multiplication of polynomials, we recommend that you enter our category of Algebra.