What are some of the examples of Expressions?

Expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

• A constant is a fixed numerical value.
• A variable is a symbol that does not have a fixed value.
• A constant, a single variable, or a combination of a variable and a constant combined with multiplication or division is defined as a Term.

Types of Expressions 

There are three types of expressions: 

Arithmetic Expression: This is the expression that includes only numbers and mathematical operators such as addition, subtraction, multiplication, division. 

Example: 80-5 x 2, 20+5, 85 – 25 …

Fractional Expression: This is the expression that includes fractional numbers and mathematical operators .. 

Example: 6/4 – 5/2 , 20/10 +25/2 etc 

Algebraic Expression: This is the expression that Contains variables, numbers, and mathematical operators.

Example: 3x + 12y , 5x + 5y etc..

Algebraic expressions are further classified into some other expressions like Monomial, Binomial, Trinomial, polynomial expressions.

Monomial Expression: An expression that has only one term is termed a Monomial expression.

Examples of monomial expressions include 5x⁴, 3xy, 2x, 5y, etc.

Binomial Expression: An algebraic expression which is having two terms and unlike are termed as a binomial expression

Examples of binomial include 2xy + 8, xyz + x², etc.

Polynomial Expression: An expression that has more than one term with non-negative integral exponents of a variable is termed a polynomial expression.      

Examples of polynomial expression include ax + by + ca, x³ + 5x + 3, etc.

What are some of the examples of Expressions? 

Answer: 

A combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division is termed as Expression.

A constant is a fixed numerical value.

A variable is a symbol that does not have fixed value.

A constant, a single variable, or a combination of a variable and a constant combined with multiplication or division is defined as Term.

Example of Expression in Algebra: 3x + 9, 5x + 10…

Some more examples of expressions are: 

Ajay told his younger brother rakesh that his age was 3 more than twice his age. so He asked him to calculate his age if his age is x years. 

With an expression. Twice the age of rakesh can be written as 2x. Now Ajay’s age is 3 more than 2x. Therefore, Ajay’s age will be written as 2x + 3.

Now expression is 2x + 3 that represents here 2 is coefficient, x is a variable, and 3 is constant

Sample Problems

Question 1: Give some examples of algebraic expressions? 

Answer:

This is the expression that Contains variables, numbers, and mathematical operators .

Example: 3x + 12y , 5x + 5y 

               2xy + 8, xyz + x²

ax + by + ca, x³ + 5x + 3

Question 2: Write expression, if the first number is 5 more than twice the second number, what is the number?

Answer: 

A combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division is termed as Expression.

lets assume the second number is x means twice the number will be 2x 

So as per the question first number will be 5 + 2x, here 5 + 2x is the expression 

Question 3: Using the (a – b)² formula in algebra, find the value of (101)².

Solution:

Given: (101)² = (102 – 1)²

Using algebra formula (a – b)² = a² – 2ab + b², we have,

                                (102 – 1)² = (102)² – 2(102)(1) + (1)²

                                                = 10404 – 204 +1

                                     (101)² = 10201

Question 4: Solve the equation 5x – 4 = 3x – 8.

Solution:

Given,       5x – 4 = 3x – 8

Adding 4 on both sides,

          5x – 4 + 4 = 3x – 8 + 4

                      5x = 3x – 4

Subtract 3x from both sides,

               5x – 3x = 3x – 4 – 3x

                       2x = -4

Dividing both sides of the equation by 2,

                    2x/2 = -4/2

                         x = -2

Question 5: Solve the equation: 2x + 10 = 5x + 20

Solution:

Given: 2x + 10 = 5x +20

Subtracting 10 from both sides 

2x + 10 – 10 = 5x + 20 – 10

                2x = 5x + 10 

Subtract 5x from both sides 

2x – 5x = 5x – 5x + 10 

     -3x = 10 

        x = – 10/3

Question 6: Using the (a + b)² formula in algebra, find the value of (11)².

Solution:

Given: (11)² = (10 +1)²

Using algebra formula (a + b)² = a² + 2ab + b², we have,

                                  (10 + 1)² = (10)² + 2(10)(1) + (1)²

                                                 = 100 + 20 +1

                                        (11)² = 121

Question 7: Identify variables , constant ,coefficients from the algebraic expression 3x² + 5x + 6?

Solution:

Given algebraic expression 3x² + 5x + 6 

here x is the variable 

3 is the coefficient of x²

and 6 is constant