In this post we will learn about the concept and components of algebraic expression along with solved examples.

This chapter is very important as it would set a base for higher mathematics.

**What are Algebraic expressions?**

It is a **collection of constants, variable and both separated by addition/subtraction sign**.

Examples of algebraic expressions:

⟹ 2x

⟹ 3y + 7

⟹ \mathtt{2x^{2} \ +\ 5x\ +\ 13}

**Types of Algebraic expression**

Given below are some of the common types of algebraic expression:

**(a) Monomial Expression**

Algebraic expression with **only one entity** is called Monomial.

**Examples**

⟹ 7y

⟹ 6xy

⟹ \mathtt{15\ xy^{2} z^{2}}

**(b) Binomial Expression**

Algebraic expression with **two entities** is called **Binomial**.

**Examples**

⟹ x + 3y

⟹ xy + yz

⟹ 4/z – 16

Note: In algebraic expression, the entities are separated by addition or subtraction sign.

Any digits/variable in multiplication or division form is one entity. Separation of entity is also possible through addition/subtraction sign.

**(c) Trinomial Expression**

Expression with **three entities** is called Trinomial.

**Examples**

⟹ x + y + z

⟹ 2 + xy + 9

⟹ xy + yz + zx

⟹ \mathtt{x^{2} y\ +\ xy\ +\ y}

**(d) Polynomial**

Any algebraic **expression with one or more entity** is called **polynomial**.

**Examples**

⟹ 2x + 5xy + 7

This is a polynomial with three entities.

⟹ \mathtt{x^{2} y}

Its a polynomial with one entity.

⟹ \mathtt{6\ +\ y^{2} \ +\ 2x\ +\ y}

This is a polynomial with four entity.

**Constants, Variables & Coefficient in Algebraic Expression**

In any algebraic expression we find three types of identity.**(a) Constant**

It’s an identity whose value is constant and doesn’t change with time.

All the numbers in math are part of the constants.

2, -9, 31, 66 etc. are examples of constant.

**(b) Variable**

Any identity whose value is not constant and changes with time is called variable.

In algebra, the variable is expressed through English alphabet.

x, y, z etc. are examples of variable.

**(c) Coefficient**

In algebraic expression, the constant part present in front of variable is called coefficient.

Example

5a ⟹ 5 is the coefficient.

\mathtt{7y^{2} \ +\ 9z\ } ⟹ 7 & y are the coefficients.

**Simplifying Algebraic expression**

In algebraic expression, **only the entities with same variable & power can be simplified further**.

To simplify the expression, follow the below rules:

(a) Take entity of same variable next to each other

(b) Add/Subtract the coefficient without changing the variables.

Let us understand the simplification with the help of examples.

**Example 01**

7x + 3y + 2x

The expression consist of three entities, with 7x & 2x have same power.

(a) Taking same variables under the bracket

⟹ (7x + 2x) + 3y

(b) Add the coefficients and keep the variable same

⟹ 9x + 3y

**Example 02** \mathtt{9x^{2} \ +\ 2y^{3} +\ x^{2} +3y}

Solution

\mathtt{\Longrightarrow \ 9x^{2} \ +\ 2y^{3} +\ x^{2} +3y}\\\ \\ \mathtt{\Longrightarrow \ 9x^{2} \ \ +\ x^{2} +\ 2y^{3} +\ 3y}\\\ \\ \mathtt{\Longrightarrow \ 10x^{2} +\ 2y^{3} +\ 3y}

**Example 03**

\mathtt{3x^{2} y+x^{3} y\ +\ 9x^{2} y+\ 3x^{3} y}

\mathtt{\Longrightarrow \ \left( 3x^{2} y+9x^{2} y\right) +\left( x^{3} y+\ 3x^{3} y\right)}\\\ \\ \mathtt{\Longrightarrow \ 12x^{2} y\ +\ 4x^{3} y}

**Example 04**

xy + 3xyz + 6xy + 5xyz + 2zx

Solution

⟹ (xy + 6xy) + (3xyz + 5xyz) + 2zx

⟹ 7xy + 8xyz + 2zx

**Example 05**

\mathtt{10x^{3} z\ +\ 3xz^{2} +x^{3} z\ +\ 4x^{3} z}

\mathtt{\Longrightarrow \ \left( 10x^{3} z\ +x^{3} z\ +\ 4x^{3} z\right) +3xz^{2}}\\\ \\ \mathtt{\Longrightarrow \ 15x^{3} z\ +\ 3xz^{2}}

**Frequently asked Question – Algebraic Expression**

**(01) Difference between algebraic expression and algebraic equation?**

Algebraic expression is a combination of constants and variables separated by addition/subtraction sign.

Algebraic equation is a type of algebraic expression with equal to “=” sign.

It tells that one side of the entity is equal to other side.

For Example;

x + y = 3x + 2

The equation says that the left side of the expression x + y is equal to the right side of expression 3x + 2.

**(02) Find the constant, variable and coefficient in the below expression.**

⟹ 2x + 7

**Solution**

The above expression consists of two entities 2x and 7.

2x ⟹ 2 is coefficient and x is variable

7 ⟹7 is a constant.

**(03) How to identify any algebraic equation?**

Whenever you see entities with combination of constant and variable, name the combination as algebraic equation.

For example, consider the entities; 9x + 13y + 2

The expression is made of combination of three entities; 9x, 13y and 2. Hence it is an algebraic expression.

**(04) Is 10y a constant or a variable?**

10y is an entity made of both constant and variable.

10y ⟹ 10 is the constant (also known as coefficient) and y is a variable.

**(05) How is algebraic expression helpful?**

Algebraic expression is very important for our daily life.

If you want to express daily activity in the form of equation, the concept of algebraic expression will be used there.

Suppose you purchased 2 potato chips & 3 soft drinks and in total you spent 50 dollars from the store.

You can express this activity in the form of equation even without knowing the cost price of chips & soft drinks.

The equation is written as:

2x + 3y = 50

Where x and y are the variables denoting the price of chips and cold drink.

Also, if you are interested in computer programming, the concept of algebraic expression will be used throughout the coding language.