An algebraic expression is a collection of one or more terms, which are separated by the signs + (plus) or / and - (minus).

Some examples of algebraic expressions are $3x, 5x^{2}, 7x +15$

### Value of an Algebraic Expression:

Value of any expression is considered to be the numerical result we get, when any integer will get substituted in place of variables of a given algebraic expression and then simplified.
It may be an expression of multiple values, into which the variables would be given different value and then simplified.

## What is an Algebraic Expression?

An Algebraic expression is an expression that consists of variables and mathematical operations along with numbers. The letter x is the most commonly used variable. The value of an expression depends on the value of its variable(s)

$x, 3x^{2}, 2x +1$ are all Algebraic expressions

### Examples on Algebraic Expressions

Given below are some examples on how to explain the value of an algebraic expression.

Example 1:

If x = 9 and y = 3, find the value of

a) x+y b) x-y c) xy d) $\frac{x}{y}$

Solution:

a) x + y

Substitute the values, x = 9 and y = 3

x + y = 9 +3

= 12

So, the value of the expression x+y is 12

b) x - y

Substitute the values, x = 9 and y = 3

x - y = 9 - 3

= 6

So, the value of the expression x-y is 6

c) xy

Substitute the values, x = 9 and y = 3

xy = 9 x 3

= 27

So, the value of the expression xy is 27

d) $\frac{x}{y}$

Substitute the values, x = 9 and y = 3

$\frac{x}{y}$ = $\frac{9}{3}$

= 3

So, the value of the expression $\frac{x}{y}$ is 3

Example 2:

If p = 8, q =1, r = 2, find the value of :

$\frac{10pq - 3qr}{4pqr - 2p}$

Solution:

Given, p = 8, q = 1, r = 2

10 pq - 3 qr = (10 x 8 x 1) - (3 x 1 x 2)

= 80 - 6

= 74

4pqr - 2p = 4 x 8 x 2 - 2 x 8

= 64 - 16

= 48

$\frac{10pq - 3qr}{4pqr - 2p}$ = $\frac{74}{48}$

= $\frac{37}{24}$

Example 3:

Find the value of the expression, 5x+3, when x = 2, 0, -2.

Solution:

The value of the expression 5x+3 depends on the value of its variable x. That is,

(i) if x = 2, the value of the expression 5x+3 would be,
(5 x 2) + 3 = 10 + 3 = 13

(ii) if x = 0, the value of the expression 5x+3 would be,
(5 x 0) + 3 = 0 + 3 = 3

(iii) if x = -2, the value of the expression 5x+3 would be,
(5 x -2) +3 = -10 + 3 = -7

In order to find the value of an expression, the variable in it is replaced by the given value for the variable and simplified. The method of doing so is called substitution!

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