Algebraic Expressions are expressions which are obtained by performing a finite number of operations like addition, subtraction, multiplication, rising to a power on symbols (terms) representing numbers.
For Example: x2, 2y2, 3w + 4xy + 5, 2x2 + 5x – 7
Classification of Expressions
We can classify expressions as follows:
Let’s discuss each one of them:
An expression with only one term is called a monomial.
For example: 2x, 3xy, 5x2y
An expression with two unlike terms is called a binomial.
For example: 2x + 1, 2x + 4y, 7x2y +2x4
But 2x + 3x is not a binomial.
As, 2x +3x=5x which is monomial.
An expression which contains three terms is called a trinomial.
For example: 2x + y + z, x2 + 2x + 2
An expression with one or more terms is called a polynomial. A monomial, a binomial and a trinomial all are polynomials.
For example: 2x, x- 5, 12x2 – y
Addition and Subtraction of Algebraic Expressions
We have two categories under addition and subtraction of algebraic expressions:
- Adding and subtracting like terms
- Adding and subtracting general algebraic expressions
We will learn the concept by taking examples:
Adding or subtracting like terms
(i) Add: 3y + 5y + 2y
= (3 x y) + (5 x y) + (2 x y)
= (3 + 5 + 2) y
= 10 y
(ii) Subtract: 14 ab - 12 ab
= (14 – 12) ab
= 2 ab
So, from the above examples we conclude the following:
- The sum of two more like terms is a like term with a numerical coefficient equal to the sum of the numerical coefficient of all the like terms.
- The difference of two more like terms is a like term with a numerical coefficient equal to the difference of the numerical coefficient of all the like terms.
Adding or subtracting general algebraic expression
(i) Add: 13x + 7y + 2x + 6a
In the given expression, we have 13x and 2x as like terms. So, we first add them.
= 15x + 7y + 6a
As there are no like terms left in the above expression, so we get the final answer as 15x + 7y + 6a.
(ii) Subtract: 30xy – 10x – 16y from 15xy + 12y + 14x.
First, we will write complete expression as
15xy + 12y + 14x – (30xy - 10x - 16y)
= 15xy + 12y+ 14x - 30xy + 10x + 16y ....(Open the parenthesis)
= 15xy – 30xy +12y + 16y + 14x + 10x …..(Writing like terms together)
= -15xy + 28y + 24x …..(Combining like terms)
As there are no like terms left in the above expression, so we get the final answer as - 15xy + 28y + 24x
Now try it yourself! Should you still need any help, click here to schedule live online session with e Tutor!
eAgeTutor.com is the premium online tutoring provider. Using materials developed by highly qualified educators and leading content developers, a team of top-notch software experts, and a group of passionate educators, eAgeTutor works to ensure the success and satisfaction of all of its students.
Contact us today to learn more about our tutoring programs and discuss how we can help make the dreams of the student in your life come true!