Binomials

When the polynomials have two term, then the names of the polynomials is called as binomials. Thus the algebraic expression which has only two term, then the names of the expression is said to be as binomials. Binomial can be expressed by the operation such as addition, subtraction. In this article, we see about the names of binomials.

Example: a + b, here the two term a and b are separated by addition operation.

Below you could see how to solve binomials problems

Example 1:

Which of the following referred as binomial math?

Option:

a) 3x + y

b) 3 * y

c) 3xy

d) 3x ÷ y

Solution:

Option a: 3x + y, addition operation makes the polynomials in two terms.

Option b: 3 * y, multiplication operation makes the polynomials in one term as 3y.

Option c: 3xy, there is one term in this polynomial.

Option d: 3x ÷ y, division operation makes the polynomials in one term.

Hence the option a has the polynomials which have only two term which said to be as binomial in math.

Answer: Option a - - - > Binomials

Example 2:

Prove when we multiply binomial with monomial we get binomial.

Solution:

Let take the binomial as (a + b) and monomial as x.

Multiply the binomial with monomial,

(a + b) * x = ax + bx. Thus we get the binomial.

Answer: Therefore we proved as by multiplying binomial and monomials we get binomial.

Below are solved example on binomials

Example 1:

What is area of square whose side is 2x + 4?

Solution:

Given: side of the square = 2x + 4

To find the area of square = (2x+4)²

Formula for square of binomial:

(a+b)² = a² + b² + 2ab

(2x+4)² = (2x)² + 4² + 2(2x) (4)

= 4x² + 16 + 16x

Answer: Area of square = 4x² + 16 + 16x

Now clear about the binomial in math.