Posted by Debora Silva

Monomial, or algebraic term, is any algebraic expression that only has multiplication between numbers and unknowns (letters that represent unknown numbers). It is the simplest form of algebraic expression and can be understood as a polynomial that contains only one term.

The application of concepts on monomials ranges from the manufacture of objects (such as a ball, for example) to more complex calculations.

The lawyer François Viète was largely responsible for the use of letters in mathematical relationships, which allowed algebraic calculations and the development of mathematics and science.

What are the parts of a monomial?

To understand monomials, we need to know their parts. They are divided into two parts: a number, called a monomial coefficient; and a variable or product of variables (letters).

Pay attention to the following examples:

  • 4y: in this monomial, we can see the coefficient (4) and the literal part (y).
  • X - Note that, in this monomial, there are no explicit numbers. In this case, the coefficient will always be 1. The literal part is the letter x.
  • It is important to note that there are still cases where the literal part is missing, and only the numerical coefficient appears. It is a monomial without a literal part. If we only have the number zero, without the literal part, it is a null monomial.

Similar monomials

As we have already seen, each monomial is divided into two parts: literal part and coefficient. If two or more monomials have the same literal part, they are monomials or similar terms.

Examples:

-5yz and ½ yz are similar monomials, since they have the same literal part (yz).
-x and 2x are also similar monomials, since the literal part equals (x).

Algebraic addition and subtraction of monomials

Monomials can only be added or subtracted if their literal parts are the same. To perform the operation, just add the coefficients and repeat the literal part.

Look carefully at the following example:

-4xy + 16xy = 20xy

The subtraction is done in the same way:

-25xy - 3xy - 5xy = 17xy.

Multiply and divide monomials

To perform multiplication and division of monomials, they do not have to be similar. Unlike addition and subtraction, these operations must be performed with both the literal part and the coefficient. We must operate the coefficients on each other and the literal part of one for the literal part of the other. Remember that exponents must be added.

Look at the following examples:

-6x²y.2x³.3y In this, we multiply 6.2.3 = 36 and then multiply x².x³.yy = x5.y²

In division, we have to divide the coefficients between them, in the same way as the literal part:

-12x4y / 3x2y -> 12/3 = 4; the literal part: x4 / x² = x² and y / y = 1, giving the result equal to 4x².