Expression and Equations are two important concepts of algebra in mathematics. We need to learn about expressions and equations to solve different types of easy and complex problems in both mathematics and real-life applications. expression is a combination of numbers, variables, and operators while an equation is a mathematical statement that maintains the equality of two expressions.
In this article, we are going to learn about expressions and equations, and also different types of expressions and equations.
Table of Content
- What is an Expression?
- Types of Expressions
- What is an Equation?
- Types of Equation
- Difference Between Expression and Equation
- Components of Expressions and Equations
- Simplifying Expressions
- Simplifying Equations
- Examples on Expressions and equations
What is an Expression?
An expression in mathematics is a combination of numbers, letters that represent numbers, and operations such as addition, subtraction, multiplication and division. The expression represents a value by combining all these. We don’t use the equality sign (=) in expressions, it is used in equations.
Example: 3x + 4y – 7
This is an expression having x and y as variables and 3, 4 and 7 as constant numbers.
Types of Expressions
There are different types of expressions. Some of them are mentioned below:
Numerical Expressions
These expressions contain only numbers and operations.
Example: 7 + 8 × 3
Algebraic Expressions
These expressions contain variables, numbers, and operations
Example: 3x2 + 7x – 3
Polynomial Expressions
These expressions contain algebraic expressions with multiple terms.
Example: 4x3 – 3x2 + 2x – 4
Rational Expressions
Expressions which have division of two or more polynomials are called as rational expressions.
Example: 1/x + 2/x + 3
Radical Expressions
Expressions which Include variables or numbers under a root sign are called as radical expressions.
Example: √3x + 7
What is an Equation?
An equation is a mathematical statement that maintain the equality of two expressions, separated by an equality sign =. We solve these equation to find the value of variable that make the equation true.
Example: x2 – 3x -3 = 0
This is an example of equation where x is variable and 1 , -3 and -3 are constants.
Types of Equation
Linear Equations
Equations of the first degree i.e. the highest exponent of the variable is 1 is known as linear equation.
Example: 3x + 4 = 12
Quadratic Equations
Equations of the second degree i.e. the highest exponent of the variable is 2 is known as quadratic equation.
Example: 3x2 – 4x + 12 = 0
Polynomial Equations
Equations which have polynomial expressions is known as polynomial equation.
Example: 4x4 + 3x2 + 1 = 0
Rational Equations
Equations which involve rational expression such as fraction.
Example: 1/x + 2/x+1 = 3
Difference Between Expression and Equation
Below is the key differences between expressions and equations in tabular form:
Characteristics | Expression | Equation |
---|---|---|
Definition | A combination of numbers, variables, and operators | A statement asserting the equality of two expressions |
Contains | No equality sign | An equality sign (=) |
Purpose | Represents a value or set of values | Shows that two expressions are equal |
Solution | cannot be solved | can be solved |
Example | 3x + 2 | 3x + 2 = 7 |
Components of Expressions and Equations
Expressions and equation are made of different components. Some of them are mentioned below:
Variables: Variables are symbol which are used to represents unknown values. Variables are usually denoted by letters such as x, y and z.
Constants: Constants are fixed values that do not changes. These are numbers such as 1, 2, 3…… They can be any specific variable that represent fixed known quantities.
Coefficients: Coefficients are numerical factors multiplied by the variables in a given expression or equation.
Operators: Operators are mathematical symbols that are used to indicate mathematical operations such as addition, subtraction, multiplication and division.
Simplifying Expressions
Simplifying an expression is writing the expression in simplest form by combining like terms and performing operations.
Below is the simple example to demonstrate this:
Simplify the expression: 3x + 4y + 2 + 2x + 9y + 3.
Solution:
For given expression we combine like terms
3x + 2x = 5x
4y + 9y = 13y
2 + 3 = 5
So, the simplified expression is 5x + 13y + 5
Simplifying Equations
We can simplify equations which involves combination of constants and variables with equality sign.
Below is the simple example to demonstrate this:
Example: 3(x+2)-4=2(x+5) Solve this equation
Solution:
First apply distribute property to simplify and expand the equation
3x + 6 – 4 = 2x + 10
Now, combine Like Terms
3x + 2 = 2x + 10
Isolate the Variable
3x – 2x = 10 – 2
x = 8
Examples on Expressions and equations
Example 1: Simplify the given expression: 2x+3x-4+7.
Solution:
We combine like terms:
2x + 3x = 5x -4 + 7 = 3
So, simplified expression is 5x + 3.
Example 2: Solve the following equation: 3x – 5 = 7
Solution:
3x – 5 = 7
Add 5 to both side of equation
3x – 5 + 5 = 7 + 5
3x = 12
x = 12/3
x = 4
Example 3: Factor the quadratic equation x2 – 5x + 6 = 0.
Solution:
Find two numbers that multiply to 6 and add to -5: these two numbers are -2 and -3 (x – 2) ( x – 3) = 0
So, factors are (x – 2) ( x – 3)
Example 4: Factor the quadratic equation x2 – 4x + 4 = 0.
Solution:
We can identify a pattern in this question:
(x)2 – (2)(2)(x) + (2)2
It is a question of pattern (a – b)2 = a2 -2ab + b
(x – 2)2 = 0
So, factors are (x – 2) ( x – 2)
Example 5: Solve the linear Equation 5x – 7 = 3x + 9.
Solution:
To solve the given linear term of given equation:
5x – 7 = 3x + 9
Subtract 3x from both sides
5x – 3x – 7 = 9
2x – 7 = 9
Add 7 to both sides:
2x – 7 + 7 = 9 + 7
2x = 16
Divide by 2:
x = 16/2 = 8
Conclusion
Expressions and equations are fundamental topics in algebra mathematics. These topics play important role in various field and everyday life. It is important to understand how to deal with expression and how to solve equations.
Also Read:
- Expressions in Math
- Equation in Maths
- Algebraic Expressions in Math: Definition, Example and Equation
- Equations with Variables
FAQs on Expressions And Equations
What is the difference between expression and equation?
An expression is a combination of numbers, letters, and operations such as addition, subtraction, multiplication and division whereas equation is a mathematical statement that maintain the equality of two expressions.
Can an equation have more than one solution?
Yes, an equation can have more than one solution. Depending on type such as linear equation has one solution, quadratic equation has two solutions and cubic equation has three solutions.
How can we verify that solution of our equation are correct?
We put value of variable again into equation and if both side of equation becomes equal then our equation is correct. This is applicable to every kind of equation such as linear equation, quadratic equation, polynomial equation etc.
What are examples of expressions and equations to show that expressions and equation are somehow related?
Example of expression:
- 3x + 2
- 8x + 7
Example of Equation:
3x + 2 = 8x + 7
Previous Article
Linear Equations Formula
Next Article
Population Variance Formula