Algebraic Expression

Monomials, Binomials, Trinomials and Polynomials

Before we move to the terms of an algebraic expression, you need to recall the definition of an algebraic expression. As discussed in the previous topic, an algebraic expression is an amalgam of variables and constants of 1 or more terms. The expressions are separated by symbols or operations like (+, –, × and ÷). These expressions are categorized as a monomial, binomial, trinomial and polynomial.

Monomials

A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too. For example, 9x3yz is a single term, where 9 is the coefficient, x, y, z are the variables and 3 is the degree of monomial.

Examples of Monomial

Let us consider some of the variables and examples:

→ p – One variable and degree is one.
→ 5p2 – with 5 as coefficient and degree as two.
→ p3q – with two variables (p and q) and degree as 4 (i.e., 3+1).
→ -6ty – t and y are two variables with coefficient -6.
             

Binomials

Binomial is a polynomial with only terms. For example, x + 2 is a binomial, where x and 2 are two separate terms. Also, the coefficient of x is 1, the exponent of x is 1 and 2 is the constant here. Therefore, A binomial is a two-term algebraic expression that contains variable, coefficient, exponents and constant.

Another example of a binomial polynomial is x2 + 4x. Thus, based on this binomial we can say the following:

                
→ x2 and 4x are the two terms
→ Variable = x
→ The exponent of x2 is 2 and x is 1
→ Coefficient of x2 is 1 and of x is 4
            

Trinomials

A trinomial is an algebraic expression that has three non-zero terms. Examples of a trinomial expression:

→ x + y + z is a trinomial in three variables x, y and z.
→ 2a2 + 5a + 7 is a trinomial in one variables a.
→ xy + x + 2y2 is a trinomial in two variables x and y.
→ -7m5 + n3 – 3m2n2 is a trinomial in two variables m and n.
→ 5abc – 7ab + 9ac is a trinomial in three variables a, b and c.
→ x2/3 + ay – 6bz is a trinomial in five variables a, b, x, y and z.
            

Polynomials

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.