Definition of a term in an algebraic expression with examples
What is a Term in Mathematics?
A term in mathematics is nothing but a single expression. The term can be a single number - either positive or negative, or it can be a variable, or it can be more than one variable multiplied together. The variables are often written with numbers in front of them and these numbers are called coefficients. Let’s have a look at a few examples:
Single number as a term: 15
A variable: a
More than one variable: 2x3y24z3
In algebra, two or more terms are often joined to make an expression. For example:
2a + 3b
4c - 5d2
6x + 7y2 - 8z3
4x2y + 5a2b3 - 6m3n4
There are two types of terms: Like terms and unlike terms. Let’s learn about them.
Like Terms
Like terms are the terms whose variables are similar. For example - 2x2 and 3x2 are like terms because the variable x2 is the same. A few more examples are: 3a3, 5a3, and 7a3; 2x2y, 3x2y, and 4x2y.
Like Terms
To solve the algebraic expressions, we need to combine the like terms and simplify the expressions. For example:
3x2 + 2x + 9 - 2x2+ 5x - 3
= 3x2 - 2x2 + 2x + 5x + 9 - 3
= x2 + 7x + 6
Would you like to solve an exercise?
Exercise on Like Terms
Here are a few questions:
2r2+1+(−4r2)+7
4x + 2y + 3x - y
-5m + (-6n) + 3m - 2n
3a2 + 5b + 6a + a2 - 2b
-z2 + 12z2 - 5z + 8z3 - 15z
Solutions:
2r2+1+(−4r2)+7
= 2r2 - 4r2 + 1 + 7
=-2r2 + 8
4x + 2y + 3x - y
= 4x + 3x + 2y - y
= 7x + y
-5m + (-6n) + 3m - 2n
= -5m + 3m - 6n - 2n
=2m - 8n
3a2 + 5b + 6a + a2 - 2b
= 3a2 + a2 + 6a + 5b - 2b
= 4a2 + 6a + 3b
-z2 + 12z2 - 5z + 8z3 - 15z
= 8z3 - z2 + 12z2 - 5z - 15z
= 8z3 + 11z2 - 20z
Unlike Terms
Unlike terms are the terms whose variables are different from each other. Example:
4x and 9y; 3x2 and 5y; 4a2 + 5b3 - 6z4
Simplifying expressions with like and unlike terms:
2ab2 - 7c2 + 3abc - 4ab2 + 8c2 - ab
= 2ab2 - 4ab2 - 7c2 + 8c2 + 3abc - ab
= -2ab2 + c2 + 3abc - ab
Like and Unlike terms
What Have We Observed?
So what have we observed? We have observed that while simplifying any expression, only the like terms are added or subtracted. The, unlike terms, remain as they are in an expression.
Did you enjoy learning about the like and unlike terms? We have other interesting math ‘magic’ topics as well for you to explore. You can explore it through our website and also download the app from the play store.
FAQs on Understanding Terms in Mathematics
1. What is a term in math?
A term in math is a single number, variable, or a product of numbers and variables separated by addition or subtraction signs in an expression. In an algebraic expression, terms are the individual parts being added or subtracted.
- In 5x + 3, the terms are 5x and 3.
- In 4a² − 7a + 2, the terms are 4a², −7a, and 2.
2. What are the different types of terms in algebra?
The main types of terms in algebra are constant terms, variable terms, and like or unlike terms.
- Constant term: A number without a variable (e.g., 6).
- Variable term: Contains a variable (e.g., 3x).
- Like terms: Terms with the same variables and exponents (e.g., 2x and 5x).
- Unlike terms: Terms with different variables or powers (e.g., x and x²).
3. What is a constant term in math?
A constant term is a term that has no variables and remains the same value. It is simply a number in an algebraic expression.
- In 7x + 4, the constant term is 4.
- In 3a² − 5a + 9, the constant term is 9.
4. What are like terms in math?
Like terms are terms that have the same variables raised to the same powers. Only their coefficients may differ.
- 3x and 8x are like terms.
- 5a² and −2a² are like terms.
- 4x and 4x² are unlike terms because the exponents differ.
5. How do you identify terms in an algebraic expression?
You identify terms in an expression by separating parts divided by addition (+) or subtraction (−) signs.
- Step 1: Look for + or − symbols.
- Step 2: Split the expression at those symbols.
- Step 3: Include the sign with each term.
6. What is the difference between a term and a factor in math?
A term is a part of an expression separated by + or −, while a factor is a number or variable multiplied within a term.
- In 4x + 5, the terms are 4x and 5.
- In the term 4x, the factors are 4 and x.
7. Can you give an example of terms in a polynomial?
In a polynomial, terms are the individual algebraic parts separated by addition or subtraction signs. For example:
- In 2x² + 5x − 7, the terms are 2x², 5x, and −7.
8. How do you combine like terms?
You combine like terms by adding or subtracting their coefficients while keeping the variable part unchanged.
- Example: 3x + 7x
- Add coefficients: 3 + 7 = 10
- Result: 10x
9. What is a coefficient in a term?
A coefficient is the numerical factor multiplied by a variable in a term. It shows how many times the variable is taken.
- In 6x, the coefficient is 6.
- In −4a², the coefficient is −4.
- In x, the coefficient is 1 (implied).
10. How many terms are in an expression?
The number of terms in an expression is counted by identifying the parts separated by addition or subtraction signs.
- In 8x + 3, there are 2 terms.
- In 4a² − 5a + 6 − 2a², there are 4 terms.
