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

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.**

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

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.

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.

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.

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.

**Example**

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

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

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

**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)

**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.**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.**How do you write an algebraic expression?****Is 5 an algebraic expression?****algebraic expression,**as it needs to have one variable and operation attached to the algebraic.**How do you simplify an expression?****algebraic expression**.The last step is to combine the like terms by addition or subtraction and the constants.