What are some of the examples of Expressions?
Last Updated :
30 Jan, 2024
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
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