 # Algebraic expressions

Algebraic expressions definition:

Before we define algebraic expressions, we first need to define the following terms:

(a) Constants: A symbol or number in algebra that has a fixed value is called a constant.

(b) Variables: A symbol in algebra that can be assigned different values is called a variable.

For example, 1/3, -8, 5,

Definition: A combination of constants and variables connected by the signs +, -, x and ÷ is called an
expression of algebra. The several parts of an expression separated by + or – signs are called the terms
of the expression. Thus 5 – 3x + 4y + 8xy + 7x^2y is an algebraic-expression containing five terms and 5x
– 7y is an algebraic-expression containing two terms.

Algebraic expressions examples:

(1) 2x + 3y

(2) x + 5y + 0.5z

(3) 8x^2y^2

(4) 2^x + x^2 - √x +1

(5) etc

Of the above expressions the expression number 4 is a little different from the other in that, that it has
the variable as an exponent. Such expressions are sometimes also called algebraic expressions with
exponents.

Algebraic expressions word problems:

Algebraic-expressions are extensively used to solve a variety of word problems. Problems of mixtures,
problems of relative speeds, problems of cost and revenues etc are some examples of problems that
can be solved using algebraic-expressions. Let us see a few examples of how to write algebraic way of
expressions.

1. Write an expression for the following phrase: the sum of a variable x and 5

Answer: x + 5

2. Write an expression for: sum of a number and twice the same number

Answer: x + 2x

3. Express in algebraic terms: the product of an integer and its successor.

, √7 etc are all constants and x,y,z, etc are all variables.

Answer: n*(n+1)

4. The length of a grape vine yard is 15 meters more than its width. Write an expression to represent
width of the yard.

Width = l – 15, where l is the length of the yard.

5. A liter bottle of soft drink was emptied into two jugs of different sizes. Write an expression to
represent the quantity of liquid in the smaller jug.

V = 1 – x, where x is the quantity of liquid in the larger jug.