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Forming an Algebraic Expression

The combination of variables (literals) and constants (numbers) including mathematical operations
(+, –, × or ÷) is known as algebraic expression.
In other words, a mathematical situation with unknown quantities (variables) and numbers are
represented as an algebraic expression.

A number expression like (4 × 3) + 5 can be immediately create and solve
evaluated as (4 × 3) + 5 = 12 + 5 = 17
Form expressions using y, 2 and 7.
But an expression like (4x + 5), which contains the variable Every expression must have y in it.
x, cannot be evaluated. Use only two number operations.
This can be evaluated only if there are given some values These should be different.
for x.
Look at the table given below for the some examples of algebraic expressions.

Expressions How Formed?
(a) x + 7 7 added to x

(b) y – 8 8 subtracted from y
(c) 10n n multiplied by 10
a
(d) a divided by 5
5
(e) –5t t multiplied by (–5)
(f) 3p + 2 first p multiplied by 3, then 2 added to the product

(g) 2q – 3 first q multiplied by 2, then 3 subtracted from the product

Quick Check
Write the statement ‘13 less than the sum of x and double of p’ mathematically.

For more clarity, study the following table.

Expressions Variable Constant Formation
2x x 2 Multiplying x by constant 2 or product of 2 and x
3y + 1 y 3 and 1 Adding 1 to the product of 3 and y

7 – 5ab a, b 7, 5 Subtracting the product of constant and variables
5, a and b from 7
x ÷ y x, y 1 Dividing x by y

p – 2q p, q 2 Substracting twice of q from the square of p
2
It is clear from the above examples that expressions are like instructions that tells us what we have
to do with a number or variable.

Sometimes you might have to describe a real-life situation using a mathematical expression.

You need to imagine what would happen to a quantity, and write that using variables and constants
with operations (+, –, ×, and ÷).

109 Introduction to Algebra