The experiment to determine Verify the Algebraic Identity (a-b)² = a²- 2ab+b² are part of the Class 9 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.
Maths Lab Manual Class 9 CBSE Verify the Algebraic Identity (a-b)² = a²- 2ab+b² Experiment
Determine Verify the Algebraic Identity (a-b)² = a²- 2ab+b² Class 9 Practical
OBJECTIVE
To verify the algebraic identity (a – b)² = a² – 2ab + b².
Materials Required
- Drawing sheet
- Pencil
- Coloured papers
- Scissors
- Ruler
- Adhesive
Prerequisite Knowledge
- Square and its area.
- Rectangle and its area.
Theory
- For square and its area refer to Activity 3.
- For rectangle and its area refer to Activity 3.
Procedure
- From a coloured paper, cut a square PQRS of side a units, (see Fig. 4.1)
- Further, cut out another square TQWX of side b units such that b < a. (see Fig. 4.2)
- Now, cut out a rectangle USRV of length a units and breadth b units from another coloured paper, (see Fig. 4.3)
- Now further, cut out another rectangle ZVWX of length a units and breadth b units, (see Fig. 4.4)
- Now, arrange figures 4.1, 4.2, 4.3 and 4.4, according to their vertices and paste it on a drawing sheet, (see Fig. 4.5)
Demonstration
From the figures 4.1,4.2, 4.3 and 4.4, we have Area of square PQRS = a²
Area of square TQWX = b²
Area of rectangle USRV = ab and Area of rectangle ZVWX – ab
Area of square PUZT = Area of square PQRS + Area of square TQWX – Area of rectangle ZVWX – Area of rectangle USRV
= a² + b² – ba-ab
= (a² -2ab + b²) …(i)
Also, from Fig. 4.5, it is clear that PUZT is a square whose each side is (a – b).
Area of square PUZT = (Side)²
= [(a-b)]² =(a-b)² …(ii)
From Eqs. (i) and (ii), we get (a – b)² = (a² – 2ab + b²)
Here, area is in square units.
Observation
On actual measurement, we get
a = ………… ,
b= ………… ,
(a-b) = ………… ,
a² = ………… ,
b² = ………… ,
(a² – b²) = ………… ,
ab = ………… ,
and 2ab = ………… ,
Hence, (a – b)² = a² – 2ab + b²
Result
Algebraic identity (a – b)² = a² – 2ab + b² has been verified.
Application
The identity (a – b)² = a² -2ab + b² may be used for
- calculating the square of a number which can be expressed as a difference of two convenient numbers.
- simplification and factorization of algebraic expressions.
Viva Voce
Question 1:
What do you mean by an algebraic identity?
Answer:
An algebraic identity is an algebraic equation which is true for all values of variables occurring in it.
Question 2:
Is (x – 3y)² = x² – 6xy + 9y² an algebraic identity?
Answer:
Yes
Question 3:
Which identity should be use to expand (3x – 2y)²?
Answer:
(a – b)² = a² – 2ab + b²
Question 4:
Is the identity (a – b) = a² – 2ab + b² hold for negative values of a and b?
Answer:
Yes
Question 5:
What do we mean by degree of an algebraic expression?
Answer:
The highest power of the variable involved in the algebraic expression is called its degree.
Question 6:
The algebraic identity is true for every real number.
Answer:
Yes
Question 7:
Suppose we want square of any natural number, then it is possible to find the square of any natural number by using the identity
(a – b)² =a² +b² – 2ab
Answer:
Yes
Question 8:
In an identity (a – b)² =a² +b² – 2ab, if both variables are equal, then find the value of (a – b)².
Answer:
When a = b, then
(a-b)² = (b-b)² =0
Suggested Activity
Verify the algebraic identity (a-b)² = a² – 2ab + b² by taking a = 9 and b = 4.
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