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Algebraic Expressions

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Introduction


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.maths_a1


Algebraic expressions contain variables and constants. A variable’s value is not fixed. On the other hand, a constant has a fixed value.

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:


Monomial

An expression with only one term is called a monomial.
For example: 2x, 3xy, 5x2y



Binomial

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.


Trinomial

An expression which contains three terms is called a trinomial.
For example: 2x + y + z, x2 + 2x + 2


Polynomial

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

            maths_a1

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 


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