Monomial Binomial

Introduction:

        In this branch of mathematics, we use letters similar to a, b, x and y to refer to numbers. Performing addition, subtraction, multiplication, division of roots on these signs and real numbers, we get what are known as the algebraic expressions. Signs in an algebraic expression are known as variables of the expression. For example, in ax + b, if a and b are particular numbers and x is not specified, then x is the variable of ax + b. In 2x2 + 3xy + y2, x and y are variables

Definitions:

Definition of monomial:

       An algebraic expression of the form axn is known as a monomial in x where a is a known number, x is a variable and n is a non-negative integer. The number a is known the coefficient of xn and n, the degree of the monomial and a monomial is an only one term which contain no symbol plus (+) or minus (-).

       For example, 5x4 is a monomial in x of degree 4 and 5 is the coefficient of x4.

Definition of binomial:

       The summation of two monomials is known as a binomial and the summation of three monomials is known as a trinomial.

       For example, 2x4+ 2x3 is a binomial and x5 – 7x4+ 3 is a trinomial.

       Other example of binomial: 6x + 5, y – q, etc.

Definition of polynomial:

       The summation of a finite number of monomials in x is known as a polynomial in x. The coefficients of the monomials within a polynomial are called the coefficients of the polynomial.

       If every one of the coefficients of a polynomial are zero, then the polynomial is called the zero polynomial.

Examples:

Examples of monomial:

Example 1:

    Which of the following expression of monomial?

Choices:

    A. 5x

    B. 2p+q

    C. 5x2 +25

    D. None of them

The correct answer: A

Example of binomial:

Example 2:

    Add the binomial expression 5x + 2y and 2x -8y

Solution:

    The given binomial expression 5x + 2y and 2x -8y

                 = 5x + 2y +2x -8y

                 = 5x+2x +2y -8y

    Add the like term we get,

                 = 7x -6y

    The answer is 7x -6y.

    These are examples of monomial and binomial.