Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions. For example, Tim’s grandma gave him many candy bars. He ate a few and now had 5 left. So, how many candy bars did Tim eat?

**Let us pose this question using algebra:**

We know how many candy bars are left, so the number 5 would be called the *constant. ***Constants** are numbers that have a fixed numerical value. We do not know how many candy bars Tim’s grandma gave him, so we will call it *x*. The letter *x* represents the unknown quantity and is known as a *variable*. When we subtract the number of uneaten candy bars from the number of candy bars Tim’s grandma gave him, we will learn how many he has eaten already.

## What Is an Algebraic Expression?

**An algebraic expression consists of unknown variables, numbers, and arithmetic operators.**

*x – 5* is a simple **algebraic expression. **When we combine constants and variables connected by mathematical operations such as +, -, x, and ÷, we get an **algebraic expression**.

Let us look at a few more **algebraic expressions**.

A coefficient is a number multiplied by the variable.The coefficient of *5** x + 10* is 5 and

*8 – **2** x *is *–*2.

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## What Is a Term in Math?

In algebra, an algebraic expression is formed by a** term** or a group of **terms** together. **Term in math** is defined as the values on which mathematical operations occur in an **algebraic expression. **Let’s understand with an example of term.

Both *8x* and 9 are terms of this algebraic expression.

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## What Are the Factors of a Term?

The factors of a term are the numbers or variables that are multiplied to form the term.

For example, the factors of the term 9xy are 9, x, and y.

## Different Terms in Algebra

There are two kinds of terms in algebra:** Like Terms** and **Unlike Terms**.

**Like Terms:** Like terms are terms whose variables and exponent power are the same. They can be simplified by combining them. The operations of addition and subtraction can be performed on them together.

For example, 5x + 8x is an algebraic expression with like terms.

**Unlike Terms: **Unlike terms are those terms whose variables and their exponents are different from each other. They cannot be simplified by combining them. The operations of addition and subtraction cannot be performed on them together.

For example, 5x + 8y is an algebraic expression with unlike terms.

Let Us Learn about ‘Polynomials’

Polynomial comprises two Greek words: the word “poly” means “many” and “nominal” means “terms”. So, we get the phrase “many terms”. Polynomials are classified into three different types based on the number of terms it consists of.

The three types of polynomials are:

- Monomials
- Binomials
- Trinomials

Monomial: It consists of only one term.

Here are a few examples of monomials:

*4x**12y**5z*

Binomial: It is a polynomial that consists of exactly two terms.

Here are a few examples of binomials:

*4x + 27**12y -3**5z+ 2x*

Trinomial: It is a polynomial that consists of exactly three terms.

Here are a few examples of trinomials:

*4x + 27 – 3z**12y -3 + 7z**5z+ 2x + 8y*

**Example 1: What are the terms, variables, and constants of the algebraic expression: **

*9x ***–*** 7y + 5***?**

## Solved Examples

**Solution:**

In the algebraic expression, *9x – 7y + 5* (Given)

The terms are *9x, -7y and 5*

The variables are *x and y*

Variables are numbers that can take various numerical values.

The constant is the number 5.

*Constants are numbers that have a fixed numerical value.*

**Example 2: What are the factors of the algebraic expression 3abc?**

**Solution:**

The factors of a term are the numbers or variables that are multiplied to form the term.

So, the factors of 3abc are 3, a, b, and c.

**Example 3: Identify the like and unlike terms:**

**a) 4p ***–** ***7q**

**b) 12y – 5y**

**Solution:**

a) 4p – 7q

These are unlike terms. Their variables are different from each other.

b) 12y – 5y These are like terms.** **Their variables are the same.

## Practice Problems

## Term in Math - Definition With Examples

### There were x number of sparrows sitting on the branches of a tree. Three flew away.

Choose the correct algebraic expression to depict the statements given above.

The number of sparrows sitting on branches of the tree is x (given). Three flew away, so the sparrows remaining are x – 3.

Therefore, the algebraic expression for the given statement is x – 3.

### What are the terms of the algebraic expression 7x – 9?

Terms are the values on which mathematical operations occur in an algebraic expression.

The terms of this algebraic expression are 7x and 9.

### What are the factors of the algebraic expression 11yz?

The factors of a term are the numbers or variables that are multiplied to form the term.

In the given algebraic expression 11, y and z are multiplied to form 11yz.

## Frequently Asked Questions

**What are the terms in an algebraic expression made up of?**

A Term in an algebraic expression can be:

- A constant
- A variable (with or without coefficients )
- Both a constant and a variable

The terms add up to form an algebraic expression. So, they are known as the components of the expression.

**What are polynomials?**

A polynomial comprises two Greek words: “poly” meaning “many” and “nominal” meaning “terms”. So, it makes up the phrase “many terms”.

**What are the types of polynomials?**

Polynomials are classified into three different types based on the number of terms they consist of. The three types of polynomials are:

Monomial: It consists of only one term. For example, 3a.

Binomial: It is a polynomial that consists of exactly two terms. For example, 3a + 7b Trinomial: It is a polynomial that consists of exactly three terms. For example, 3a + 7b – 5c