What are Algebraic Expressions?

What are Algebraic Expressions?

Algebraic Expressions Introduction:  

 

An operator is a symbol that shows a mathematical operation. 

For example, the symbols, “+”, “-”, “*”, “/” ; describe what we want to do with the values, wherever above symbols are present.  

 

A term is either a variable or a single number, or variables and numbers multiplied together.  

For example: X, 2X, 3Y or 5. 

 

When an operator is put in between two terms, it becomes expression. So, expression is defined as group of terms separated by operator. 

 

3 X- 8 is an expression.  

 

Expressions can be formed by numbers as well as (instead of variables)  

In case of forming expression using only numbers,à 5 + (6 - 3)  

In case of forming expression using variables and numbers, then we have  

 5 m + 9 

 

Such expressions where both constants and variables are included are called algebraic expressions. 

Example: 

3x + 2y - 5z= 10. What is expression and terms here? 

Solution 

3x + 2y - 5z is an expression. 

Various terms of the expression are: 3X, 2Y, 5Z, 10 

 

Note: 

  • The expression containing only one term is called monomial.  

Example: 5x 

  • The expression having two terms is called binomial.  

Example: 5x + 10 

  • The expression containing three terms is called trinomial.  
            Example: 2a + 3b - 4 

  • The expression containing more than three terms is called polynomial as there is no special name for expressions containing more than three terms. 

Example:3x + 4y – 8z + 7 

  • All monomials, binomials and trinomials are ALSO polynomials.  

 

 

 

Value of an Algebraic Expression: 

If we assign values to the symbols or letters of algebraic expression then we can calculate the value of an algebraic expression.  

Let us understand the concept by following example: 

If a =6, b= 7 and c=8. Calculate the value of a + b- c. 

By putting given values of a, b and c in the algebraic expression: (a+ b- c), we get 6+ 7 -8 This is equal to 5. So the value of given algebraic expression (a +b- c) is 5. 

 

Example: Calculate the value of algebraic expression:  

(10x+ 3y- 4) if x=2 and y=1 

 

Solution 

The given algebraic expression is (10x + 3y- 4) 

By putting the respective values of (x=2) and (y=1) in the algebraic expression, we get 

= (10 × 2) + (3 × 1) - 4 

After solving parenthesis, we get 

=20 + 3 – 4 

 =19 

 

Example 12: Evaluate the algebraic expression: 3x+ (13-y) - 4z. If x=2, y=4, z=3 

 

Solution: 

The given algebraic expression is 3x+ (13-y) - 4z 

By putting the respective values of (x=2), (y=4) and (z=3) 

in the algebraic expression, we get 

= (3* 2) + (13 -4) – (4*3) 

After solving parenthesis we get 

=6 + 9 – 12 

 =3 

So, the value of expression is 3. 

 

Like and Unlike Terms 

The terms whose variables are same are called like terms. 

For example, 10x, 2x, 4x. All these terms have x and same power of x. So these terms can be easily added and subtracted like 10x + 2x +4x =16x.  

Compare this to the above situation - Yasin bought 10 eggs, Samy bought 2 eggs and Amna bought 4 eggs. So, all three, together, have bought the same/like item which is egg.  Hence it can be added. It was easier to write eggs in place of x.  

Unlike terms are those terms which have different variables. 

For example, 10x and 4y. These two terms have two different variables, therefore those are unlike terms. It can be understood such as in following example, ie, 10 oranges and 4 apples are not like quantity. So for all future reference when one or more terms in an algebraic expressions have completely different variables, then they are called unlike terms. 

 

Example: 

State whether following pair of terms are like or unlike terms? 

  • 11mn, 13mn 

  • -3x,x 

  • 4xy + 2yx 

  • 5ab + 6b 

 

Solution 

 

 

Did You Know? 

Basketball has a strong association with Algebra. Davidson College associate math professor Tim Chartier developed algebraic formulas for the NCAA basketball tournament. Even the famous NBA  
24-second shot clock was also created using an algebraic equation. 


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