# Algebraic Expression

An algebraic equation is an equation that includes one or more variables. Any expression that contains letters, numbers and algebraic operations, addition(+), subtraction(-), multiplication(×), division(÷) and exponentiation to rational exponent is called an Algebraic Expression. Expression is a sentence of words, it may have a literal meaning. In mathematics it specifically refers to all possible constants, variables and associated operations or any of the combinations between them.

## Algebraic Expression Definition

An algebraic expression may refer to constants or variables or the combinations of both with associated operators. Variables are used to represent unknown quantities. In another way we can define algebraic expression as an algebraic model of a verbal model of a statement.
To understand clearly what is an algebraic expression, let us see an example:
Solved Example
Question: If the sum of two numbers is equal to 10. What are the numbers?

Solution:
let us assign the variable ‘x’ for one number

and variable ‘y’ for another number

Thus the part of the given verbal statement ‘sum of two numbers’ can algebraically be written as ’x + y’.

ie x + y = 10

On substituting value of x, we will get the value of y.

if x = 6 then 6 + y = 10, y = 10 - 6 = 4

So the values of x and y are 6, 4 respectively.

## what is algebraic expression in math

While studying the algebraic expression first question arises in our mind, what is an algebraic expression. Algebraic expression is a set of constants, variables and operators with or without combinations, algebraic expressions can be in different forms.
The following are a few examples that illustrate different types of expression.

x + y is an expression that involve an addition.

x * y is an expression involving a multiplication.

an  is called a power expression, if ‘a’ is a real number and n is a positive integer.

ax is called as exponential expression because in this case the variable is at the place of exponent.
Solved Example
Question: Algebraic expression ‘x – y’ means ‘the difference of two quantities’

Solution:
Suppose we say x = 10 and y = 4, then the expression transforms as ’10 – 4’, which is operational now.

The difference of 10 and 4 is 6

Hence the value of the expression ‘x – y’ is 6 when x = 10 and y = 4.

This process is called ‘evaluation of algebraic expression’.

## An algebraic expression

An expression may contain various variables and constants connected by different operators. In some cases, the same expression can be transformed into another expression without change in the evaluation of the expressions. The process of such transformations is called simplification of algebraic expression or solving algebraic expression. Algebraic identities, knowledge of algebraic properties, order of operations and inherent properties of some expressions help us in simplification of expressions. The exponential expressions and logarithmic expressions can be simplified by using their properties.

For example, (xy + x) can be simplified as x(y + 1) by use of distributive property.

Similarly ln (x) + ln (y) can be simplified as, ln (xy) by use of logarithmic property.

The simplification of algebraic expressions helps a lot in solving for the variables. Mathematicians framed a rule for knowing the correct order which is known as the order of operations. It is abbreviated as PEDMAS, to indicate the correct order for simplifying an algebraic expression.
• "P" indicates that first the terms inside the parentheses must be simplified.
• "E" indicates evaluate all the exponents.
• "D" indicates division.
• "M" indicates multiplication.
• "S" indicates subtraction.
Example:

8 ÷ 4 * 2 must be simplified as (8 ÷ 4) * 2 = 2 * 2 = 4

and not as  8 ÷ (4 * 2) = 8 ÷ 8 = 1.
Solved Example
Question: If the statement is ‘4 more than twice the number is same as 10 reduced by the same number’.

Solution:
Let us assume the number as x.

4 more than twice the number is expressed as an algebraic expression as 2x + 4.

Similarly ‘10 reduced by the same number’ in algebraic expression form is 10 – x.

Since it says ‘is same as’, the two expressions are equal. That is, we can form an equation as,

2x + 4 = 10 – x.

Now with our knowledge in algebra we can simplify and solve as x = 3. Thus we find the unknown number as 3.

## Define algebraic expression

Algebraic expression is defined by the Variables x ,y and constants.