Class 7 RS Aggarwal Chapter-6 Algebraic Expressions Solutions - Free PDF Download

Algebraic expressions are equations that result from operations such as addition, subtraction, multiplication, division, and so on by any variable. Assume Yash and Harsh were playing with sticks and came up with the idea of making number patterns out of them. Yash made the number 4 out of four sticks. Harsh arranged three more sticks to make a pattern with two 4s. They realised they could keep adding three sticks in each round to make one more four. They deduced from this that they need 4+ 3(n-1) sticks, in general, to make a pattern with n number of 4s. 4+ 3(n-1) is referred to as an algebraic expression in this context.

What Exactly are Algebraic Expressions?

An algebraic expression (or variable expression) is a term that has been combined using operations such as addition, subtraction, multiplication, division, and so on. Let’s look at the expression 4x + 8 as an example. As a result, the algebraic expression 4x + 8 is an example. An algebraic expression is made up of various parts. 

Terms, Coefficients, Variables, and Constants

• A variable is a symbol in mathematics that does not have a fixed value. It can be of any value. In the preceding example involving sticks, n is a variable that can take the values 3,4,5,... Variables in mathematics include c, d, e, x, y, z, and so on.

• A constant, on the other hand, is a symbol with a fixed numerical value. Numbers are all constants. Constants include 2, 8, -(2/5), √4, and so on. 

• A term is a variable by itself (or) a constant by itself (or) a combination of variables and constants by multiplication or division. 4x2, -(3y/5), √(8y), and other terms are examples.

• In this case, the variables are multiplied by 4, -3/5, and 8. These are known as coefficients.

How Can Algebraic Expressions Be Simplified?

We simply combine like terms to simplify an algebraic expression. As a result, similar variables will be combined. The same powers will now be combined from the like variables. Take, for example, an algebraic expression and try to reduce it to its simplest form to better understand the concept. Let us put it this way:

 x3 + 5x2 − 4x3 + 4x − x2 + 5 − x

 = (x3 − 4x3) + (5x2 − x2) + (4x − x) + 5

 = −3x3 + 4x2 + 3x + 5

Hence, the algebraic expression  x3 + 5x2 − 4x3 + 4x − x2 + 5 − x simplifies to −3x3 + 4x2 + 3x + 5.  

Formulas of Algebraic Expression 

Algebraic formulas are derived from short formulas that assist us in quickly solving equations. They are simply a rearrangement of the given terms to create a more memorable expression. Below is a list of some of the most commonly used basic formulas. Take a look at this page to get a better understanding of the algebraic formulas.

• (a + b) = a2 + 2ab + b2

• (a - b) = a2 - 2ab + b2

• (a + b)(a - b) = a2 - b2

• (x + a)(x + b) = x2 + x(a + b) + ab

RS Aggarwal Solutions for Class 7 Maths Chapter 6

1. Exercise (Ex 6A) 6.1

2. Exercise (Ex 6B) 6.2

3. Exercise (Ex 6C) 6.3

A Quick Recap of the definitions that are already discussed in Class 6:

Variables - An unknown entity is called a variable when it changes with a change in the situation.

Constants - Constant never changes its value, it remains fixed.

Terms - The entities that are either added or subtracted are called terms.

Coefficients - The number with which the variable is multiplied.

Like Terms - Terms having the same variables.

For example - 3y, 7y, 45y

Unlike Terms - Terms that have different variables.

For example - 3xy, 6x, 7y

Addition and Subtraction in Algebra

1. Like Terms

The coefficients of all the terms are added or subtracted.

2x + 4x - 3x - 6x = ?

2x + 4x - 3x - 2x = x

2. Unlike Terms

All the terms with similar variables are taken together and then, the coefficients are added or subtracted.

2xy - 3x + 4x + 5y - 6xy = ?

(2xy - 6xy) + (-3x + 4x) + 5y = -4xy + x + 5y

3. Number Patterns

• The successor of a natural number, n = (n+1). Example : If n = 12, then the successor = (n + 1) = 13.

• 2n is an even number ( if n is a natural number).

• (2n+1) is an odd number.
  

4. Algebraic Expression

An algebraic expression is formed with the help of operators i.e addition, subtraction, multiplications, and divisions.

5. Equation

When an equality sign is used between two expressions, then it is called an equation.

Example: 3 + 4x = 15.

Example: Form an algebraic expression: x is first multiplied by 6 and then 7 subtracted from the product.

Solution: (6*x) - 7 = 6x - 7

Example: Let an algebraic expression be 3m²-4m+2 with variable m. Find the value of the expression if m = 2.

Solution: 3(2)² - 4(2) + 2 = 3*4 - 8 + 2 = 12 - 8 + 2 = 6.

Types of Algebraic Expression

Based on the number of terms:

Monomial Expression - Expression with only one term.

Example: 3xy, 4x², 56y

Binomial Expression - Expression with only two terms.

Example: xyz + 3y², x²y² + 3xy

Trinomial Expression - Expression with more than two terms.

Example: xyz + x²y + y²z + z²

General Formulae

1. (a + b)² = a²+ 2ab + b²

2. (a - b) ² = a² - 2ab + b²

3. (a + b) (a - b) = a²- b²

4. (a + b)³ = a³ + b³+ 3ab (a + b)

5. (a - b) ³ = a³ - b³- 3ab (a - b)

6. x³ + y³ = (x + y) (x² - xy + y²)

7. x³ - y³ = (x - y) (x² + xy + y²)
   

Preparation Tips

1. First, go through the chapter thoroughly and cover all the topics.

2. Note down all the important formulae and try to learn them.

3. Start solving the exercise questions without any guidance from anyone.

4. Try the questions at least 3 times if you are unable to solve them.

5. Seek help from Vedantu’s solution to check your answers and solve the ones that you were unable to solve.