# Chapter 12 – Algebraic Expressions

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

In class VI, we learned the basics of algebraic expressions and simple expressions, like +2xy, +3y, -5y, 4x+5, etc. Here, we will explore in detail what algebraic expressions are, how expressions are formed, terms of an expression, finding the value of an expression, addition and subtraction of algebraic expressions and using algebraic expression formulas and rules.

#### Algebraic Expressions

Let’s first understand the concept of variables and constants to understand algebraic expressions.

Variables are denoted as x, y, x, m, n, l, p, q, etc. A variable can take different values as it is not fixed.

Constants can be valued as 5, -6, 8, 12, -45, -76, -87, 96 and so on.

To get an algebraic expression, both variables and constants are combined. The variables and constants are operated as subtraction, addition, multiplication, or division to derive an algebraic expression.

Examples

• 7xy + 5
• x2 y
• 4×2 – 5x
• 4xy + 7
• 4x + 5

#### How are Expressions Formed

It is an interesting concept to understand how algebraic expressions are formed. These expressions are made with a combination of variables, constants, and coefficient.

Example
“4x+3”

Here in the above algebraic expression,

• 4 is a coefficient for the variable X. It is a constant value and is well defined with the variable.
• X is the variable as it has no fixed value and can be taken as any value.
• 3 is the constant term that has a fixed and well-defined value.

#### Terms of an Expression

Parts of an expression that are first formed separately and then added are known as terms of an expression. Let’s see an example below to identify what the terms to the algebraic expressions below are.

Example –
2×2 + 7xy

In the algebraic expression above, the terms are as below:

• The term 2×2 is a product of 2, x and x.
• The term 7xy is a product of 7, x and y.

4x+7y2+5xy

In the algebraic expression above, the terms are as below:

• The term 4x is a product of 4 and x.
• The term 7y2 is a product of 7, y and y.
• The term 5xy is a product of 5, x and y.

#### Factors of a Term

If 5pq are the terms, then its factors are 5, p, and q.

If 7×2 are the terms, then its factors are 7, x, and x.

Factors of the terms are the variable, constants, and the coefficient that form the terms expressions.

#### Like and Unlike Terms

If 2x + 3xy + 4x + 7 is an algebraic expression, then –

Like terms are 2x and 4x, and unlike terms is 3xy.

• When terms have the same algebraic factors, they are like terms.
• When terms have different algebraic factors, they are unlike terms.

#### Finding the Value of an Expression

Example

Let’s find the values of the following expressions for x = 2.

1. x + 5
2+5
3
2. 7x – 3
7*2-3
14-3
11

#### Addition and Subtraction of Algebraic Expressions

1. Subtract 24ab – 10b – 18a from 30ab + 12b + 14a.
Solution:
= 30ab + 12b + 14a – (24ab – 10b – 18a)
= 30ab + 12b + 14a – 24ab + 10b + 18a
= 30ab – 24ab + 12b + 10b + 14a + 18a
= 6ab + 22b + 32a

2. Add 3x + 11 + 8z and 7x – 5.
Solution:
= 3x + 11 + 8z + 7x – 5
= 3x + 7x + 11 – 5 + 8z

#### Using Algebraic Expression Formulas and Rules

Algebraic expressions are also used to develop formulas and rules for maths and geometry.

Algebraic expressions in formulas are used as:

• The perimeter of a square = a + a + a + a = 4a, where, a is the length of each side.
• The perimeter of a rectangle = 2(L+B), where L is length and B is the breadth of the rectangle.
• The perimeter of the equilateral triangle = 3l
• The perimeter of a square = 4l
• The perimeter of a regular pentagon = 5l
• The area of the rectangle = l × b = lb
• The area of the triangle = B*H/2

Algebraic expressions in rules are used as:

• (a + b)2 = a2 + 2ab + b2
• (a – b)2 = a2 – 2ab + b2
• a2 – b2 = (a – b)(a + b)
• (a + b)3 = a3 + b3 + 3ab(a + b)
• (a – b)3 = a3 – b3 – 3ab(a – b)
• a3 – b3 = (a – b)(a2 + ab + b2)
• a3 + b3 = (a + b)(a2 – ab + b2)

#### FAQs

1. How do you explain algebraic expressions?
Algebraic Expressions are made using variables, constants, and coefficients. These expressions are made by algebraic operations of addition, subtraction, multiplication or divisions.
2. How do you solve algebraic expressions?
Algebraic expressions are solved by first simplifying the equations and then through algebraic operations of addition, subtraction, multiplication, or divisions.
3. How do you write an algebraic expression?
30ab + 12b + 14a – (24ab – 10b – 18a)
4. Is 5 an algebraic expression?
No. 5 is not an algebraic expression, as it needs to have one variable and operation attached to the algebraic.
5. How do you simplify an expression?
The first step is to remove any grouping symbol of brackets and parentheses in the expression by multiplying factors.The second step is to use the exponent rule to remove grouping if there are exponents in the algebraic expression.The last step is to combine the like terms by addition or subtraction and the constants.

We hope it was a fun experience for you to learn about algebraic expressions and their different concepts. To learn other class VII math concepts, download the MSVgo application available on Google Play and App Store. It is a video library that explains concepts with examples, explanatory visualisations and animations.

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### High School Math

• Algebra – Arithmatic Progressions
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### Middle School Science

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### Middle School Math

• Addition
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