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# Term|Definition & Meaning

## Definition

A **term **is any **single** number or variable. An **expression **contains two or more terms. If two **numbers** or **variables **or both are multiplied by each other, we consider them as a single **term**. Since **division **can be converted into **multiplication **and vice versa, division also does not separate terms. Therefore, in an **equation**, **terms **are only separated by the +, -, and = signs.

A **term **in **mathematics **is a numerical or **algebraic expression **that represents a value or a set of values. It is used to describe the components of a **mathematical **equation or formula.

Numbers, variables, and mathematical **operations **like addition, subtraction, multiplication, and division can all be incorporated into **terms**. For instance, the **terms **“3x” and “2y” both reflect values that can change depending on the **precise **values of “x” and “y” in the equation “3x + 2y = 6.”

## Degree of a Term

The **degree **of a term is yet another **crucial** idea in terms. The **highest power **of a **variable **within a term is referred to as the **term’s degree**. For instance, the **degree **of the term 3x^{2} is 2, the degree of the term 2x is 1, and the degree of the term 7 is zero. Whereas the degree of the expression 3x^{2} + 2x + 7 is the degree of the term with the highest power, i.e., 2.

The sort of **function **that an **expression **expresses is identified by the **degree **of a term. For instance, a **quadratic **function is an expression with **terms **of degree 2, whereas a **cubic function **is an expression with terms of degree 3.

## Factors of a Term

The following are some of the properties of the factors of a term:

- A
**term’s**factors are the**numbers**or variables that are multiplied to create it. For instance, the word**3ab**has the elements 3, a, and b. - It is impossible to
**factorize**the elements further. One cannot, for instance, write 3ab as the**product**of the numbers 3 and ab. This is due to the fact that ab can be reduced to a and b. - The factors of the
**term**5x^{4}are 5, x, x, x, and x. **1**is not considered a separate**variable**.

## Types of Terms

**Terms **can be divided into **like **terms and **unlike **terms. We can also categorize **expressions **on the basis of the **number** of **terms **they entail. They are **monomials**, **binomials, **and **polynomials**.

### Like Terms

Like **terms** are those with the same **variable **or variables raised to the same **power **(s). By adding or subtracting their **coefficients**, like terms can be combined or made simpler (numerical values).

For instance, the terms 3x^{2} and 4x^{2} are **like terms **in the **expression** 3x^{2} + 4x^{2} because they both have the **variable **x raised to the same **power **2. This expression can be simplified by adding the **coefficients **of the like terms as:

3x^{2} + 4x^{2} = 7x^{2}

The terms “5x” and “2x” are **like** **terms** in the **expression **“5x + 2x” because they both have the **variable **“x” raised to the same **power** 1. This expression can be simplified by adding the **coefficients **of the like terms as:

5x + 2x = 7x

Regardless of the **coefficient **values, **like terms **are terms that have the same variables raised to the same powers. Expressions and equations can be made simpler by combining like terms by adding or removing the coefficients from each other.

### Unlike Terms

**Terms **with various variables or **variables **raised to different **powers **are considered to be unlike terms. In contrast to like terms, unlike **terms **cannot be combined by merely adding or subtracting their coefficients.

For instance, the **terms **“3x” and “4y” in the statement “3x + 4y” are **unlike terms **since they each have a unique **variable**. The **coefficients **of these **terms **cannot be added or subtracted to simplify them further.

The **terms** “5x^{2}” and “2x” in the expression “5x^{2} + 2x” are also **unlike terms **because they have the same **variable **“x” raised to different **powers **(2 and 1, respectively). The **coefficients **of these **terms **cannot be added or subtracted to simplify them further.

**Unlike terms **must remain as separate terms in an **expression **or **equation **since they cannot be combined by simply adding or subtracting their coefficients.

## Terms in Algebra

In **algebra**, terms are often used to **simplify **expressions and to help find **solutions **to equations. For instance, the expression “3x + 2y + 7z” can be **simplified **into the form “3x + 2y + 7z = k,” where “k” is a constant value. The **expression **on the left side of the equation represents a set of terms that are related to each other and can be **manipulated **to find the solution.

In addition to **variables**, terms can also include **constants**, which are values that do not **change**. For example, in the equation “3x + 2 = 7,” the term “2” is a **constant **value.

Terms can also be **combined **or **grouped **together in various ways. For example, in the equation “3x + 2y + 7z = k,” the terms “3x” and “2y” can be grouped together as “3x + 2y” and the **entire **expression can be written as “(3x + 2y) + 7z = k.” **Grouping **terms in this way can help **simplify **expressions and make them **easier **to manipulate.

## Terms in Calculus

**Calculus **also uses terms to explain the **elements **of a function. A function in **calculus **is a mathematical model that gives each **input value **a specific **output value**. **Equations **can be used to **express **functions, and the **terms **in the equation stand in for the parts of the function.

For **instance**, the terms “3x” and “2” in the equation “y = 3x + 2” stand for the **slope **and y-intercept, respectively, of the function.

## A Quick Summary

The **concept** of terms is **essential **in mathematics. They are applied to **model functions**, simplify expressions, and **describe **the elements of equations. In order to **solve **mathematical problems and comprehend the underlying **concepts **of different mathematical fields, it is critical to **understand **terms and how they can be combined and used.

## Solved Examples Involving Terms

### Example 1

Identify how many terms, **like **terms, and **unlike **terms are there in the following equations:

9a + 6b

4p^{2} + 3p + 4q + 8p + 10p^{2}

3xyz

### Solution

9a and 6b are the **two **terms in equation 9a + 6b. However, **despite **having two **unlike **terms with the variables a and b, there are no **like **terms.

The equation 4p^{2} + 3p + 4q + 8p + 10p^{2} has 5 terms. Despite having 3 **unlike **terms, there are only 2 **like** terms. In contrast, when it is reduced, it becomes:

= (4p^{2} + 10p^{2}) + (3p+ 8p) + 4q

= 14p^{2} + 11p + 4q.

Despite having three **unlike **terms with the variables p^{2}, p, and q, there exist **three **terms with no **like** terms.

In equation 3xyz, there is only **one **term. However, since there are no **additional **terms to compare it to, there are no **like **and **unlike **terms.

### Example 2

In the following algebraic expression:

2x – 5y + 8

what are the **terms**, **variables**, and **constants**?

### Solution

In the mathematical expression 2x – 5y + 8, the **t****erms** are 2x, -5y, and 8.

Both x and y are **variables**. Numbers with **multiple **possible numerical values are called **variables**.

The number 8 is a **constant**. Numbers with a **fixed** numerical value are known as **constants**.

*All images/mathematical drawings were created using GeoGebra.*