Expressions in math are combinations of numbers, variables, operators, and sometimes parentheses that represent a particular value. An expression is a statement involving at least two different numbers or variables and at least one operation, such as addition, subtraction, multiplication, division, exponents, and roots.
An expression in mathematics is a finite combination of constant or variable using operators such as addition (+), subtraction (-), multiplication (×), or division (÷).
Unlike equations, expressions do not contain an equality sign ('='). Some examples of expression include:
- 2x + 3y
- 5a − 2b
- 3/4 x + 2
- 7 + 2 × 5
Some key points regarding expressions are:
- Expressions do not contain an equality sign ("=")
- Constants, variables, or products of variables and constants are considered terms
- When a variable is multiplied by a constant, the constant is referred to as a coefficient
Terms used to Explain Expression
Some common terms used in the explanation of expression are:
- Variable
- Constant
- Coefficients
Variable
A symbol that has variable values or that can be assigned different numerical values is called a variable in an algebraic expression.
Typically, a letter from the English alphabet is used to represent a variable. For instance, x, y, z, i, c or a, b, c, etc.
Constant
A symbol in an algebraic expression with a fixed numerical value is called a constant.
For instance, 7, -5, and 0, 3/5, etc. are all constants.
Coefficients
In mathematics, a coefficients are a multiplicative factor involving a number or a variable in the term of a polynomial, series, or expression.
Coefficients can be either numeric values (constants) or letters standing for constants. For instance, in the term 7x, the coefficient is 7, and in -9y2, the coefficient is -9.
Note: Coefficients can be positive, negative, real, complex, rational, irrational, decimal, or fractional.
How to Write Expression in Math?
To write an expression in math, you need to use a combination of numbers, variables, and operational symbols.
Step 1: Interpret the given text or phrase, identifying key words related to arithmetic operations (e.g., addition, subtraction, multiplication, division)
Step 2: Replace those key words with appropriate mathematical symbols (e.g., +, -, ×, ÷).
- and with "+"
- from with "-"
- of with "×"
- by with "÷"
Step 3: Apply the order of operations when necessary, especially when dealing with multiple operations in a single expression.
Step 4: Simply to obtain the final Expression.
For example, to write the expression for "The sum of 7 and the product of -2 and x": 7 + (−2 × x) = 7 - 2x
Types of Expression
Expressions are mathematical statements that combine variables, constants, and operators. There are different types of expressions, including:
- Numerical Expression
- Algebraic Expression
- Radical Expression
- Fractional Expression
Numerical Expression
A numerical expression is a specific type of mathematical expression that involves numerals (constants) and arithmetic operations.
It produces a result that is either a number or a Boolean value when evaluated. Some examples of numerical expressions include:
- 5 - 2 + 1/2 (a simple constant expression)
- 5 + 2 - (3 × (-1) + 7) (this can be simplified to 3)
- 3 × (8 + 4) - 7 (this can be simplified to 29)
Algebraic Expression
An algebraic Expression is a mathematical expression that consists of variables, constants, and algebraic operations such as addition, subtraction, multiplication, division, and exponentiation.
Some examples of algebraic expression are:
- 3x - 3xy3 (monomial expression)
- 5xy + 8 (binomial expressions)
- ax + by + c (polynomial expressions)
Fractional Expression
A fractional Expression contains fractions within an algebraic expression. For instance, consider the following examples:
- 3/x + 9/20
- (x - 2)/(x + 2) + 2
- 3/(x - 3) - 1/2
- 4x2/(x - 5)
Radical Expression
A radical expression is a mathematical expression that contains a root symbol, such as a square root, cube root, or fourth root. Examples of radical expression include:
- 3√(2) - 7
- √(9x2) + 1/2
- √(x2 + 2x - 1)
Examples of Expression
There can be various examples of expression involving various functions, constant or variable. Some common examples include:
Polynomial Expression
All the expression of form with any degree is called polynomial expression. Some examples of polynomial expressions include:
- 2x2 + 3x + 7
- a2 + 2ab + b2
- x4 - 2xy2 + 3y4
- x3 - 8x - 11
- 3x2 - 5x3 + 8x + 9x2 - 7x + 2x3
- 2p2 - 7
- 6m3 - mn + n2 - 4
Trigonometric Expression
Expression containing trigonometric ratios is called trigonometric expression. Examples of trigonometric expression are:
- sin2x - 2sin x
- sin x + cos x + tan x
- sin3x - sin2x + sin x
- \frac{tan \theta}{\cosec \theta} + \frac{sin \theta}{\cot \theta} + \frac{cos \theta}{\cot \theta}
Logarithmic Expression
A logarithmic expression typically includes a logarithm function, denoted as either logb (x), where b represents the base of the logarithm. Some examples are:
- log10 100 - log10 10 + log10 2
- ln x + ln y -ln 2
- logπ (π2) - log10 100
Exponential Expression
Exponential expressions involve exponents and are used to represent repeated multiplication. Some examples of exponential expression are:
Factors of Expression
A factors of an expression is a number or expression that divides the expression evenly.
For example, in the expression 2x + 4, both 2 and x + 2 are factors of the expression. Some more examples of factors of expression are:
- For 3ab + 6c, factors are 3 and ab + 2c.
- For x2 - 5x + 6, (x - 2) and(x - 3) are the factors.
- For 2ab - 6ab2, 2b and a + 3ab are the factors.
Equation vs Expressions in Math
Key difference in equations and expression in math is given below:
| Feature | Equation | Expression |
|---|
| Structure | Two expressions connected by an "equal to" (=) sign. | Combination of numbers, variables, and operation symbols. |
|---|
| Number of expressions | Two | One |
|---|
| Purpose | Represents an equality between two mathematical statements. | Represents a value or a calculation without requiring equality. |
|---|
| Solution | Often solved to find a specific value for a variable. | Can be simplified to obtain a final value. |
|---|
| Example | 2x + 5 = 11 | 3x2 - 2y |
|---|
| Real-world use | Balancing chemical equations, finding distances, calculating speed, etc. | Representing areas, sums, volumes, etc. |
|---|
Articles Related to Expressions in Math:
Solved Examples on Expressions
Example 1: Find the coefficient of term 7y in the expression 6x2+ 7y + 3.
Solution:
Coefficient of term 7y in the expression 6x2+7y +3 is "7".
Example 2: Find the terms in the expression 5x +6y +3.
Solution:
No. of terms in the expression is 5x , 6y, 3.
Example 3: Find the factors in the expression 7x3+ 5x2+ 6x + 2.
Solution:
Factors in the expression are 7, x3, 5, x2, 6, x, 2.
Example 4: What type of algebraic expression is 4x + 5?
Solution:
4x + 5 has two monomials 4x and 5 and hence it is a binomial. Now, since every binomial is a type of polynomial.
Therefore, 4x + 5 is a binomial.
Example 5: Identify the terms and coefficients in the expression 3a2 +2ab.
Solution:
There are two terms in the expression 3a2, 2ab.
Coefficients in the expression are 3, 2.
Similar Reads
What are Terms in an Expression? Let us learn about what an algebraic expression is before learning about the terms of an algebraic expression. An algebraic expression is a concept of expressing numbers by using letters such as a, b, m, n, x, y, z, etc. without specifying their actual values.An algebraic expression is a mathematica
8 min read
Solving Expressions with Exponents Solving expressions with exponents involves understanding and applying rules such as the product of powers, quotient of powers, and power of a power. For instance, am × an = am+n and (am)n = amn. These properties simplify complex calculations. For example, (23)2 × 2−4 simplifies to 26−4 = 22 = 4. Un
4 min read
Expressions with One or More Variables Expression with one or more variables is an important mathematical concept. It forms the foundation of algebraic mathematics. It is important because it is used in various real-life applications. Expression with one or more variables is used in solving problems in physics, working with data in compu
8 min read
Simplify the expression (5ab)/(10ab) Algebra is the branch of mathematics that deals with the study of various symbols which represent such quantities as do not have a constant value or quantity associated with them, instead they tend to vary or change over time with respect to some other factor. Such symbols are regarded as variables
5 min read
Simplify the expression (11/10/22) × z Algebra is the study and manipulation of mathematical symbols. The expressions of algebra are composed of known numbers and unknown values. These unknown quantities are determined by some basic algebraic operations. Some of the basic standard formulas are derived to carry out these calculations. Alg
3 min read
Types of Algebraic Expressions An algebraic expression is an expression composed of various components, such as variables, constants, coefficients, and arithmetic operations. These components form various parts of the algebraic expressions.For example:3x + 52a2 − 4b + 75(x + 2) − 3Note: The highest power of the variable is known
2 min read