The experiment to determine Verify the Algebraic Identity a² – b² = (a+b) (a-b) 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 a² – b² = (a+b) (a-b) Experiment
Determine Verify the Algebraic Identity a² – b² = (a+b) (a-b) Class 9 Practical
OBJECTIVE
To verify the algebraic identity a² – b² = (a+b) (a-b).
Materials Required
- Drawing sheet
- Pencil
- Colored papers
- Scissors
- Sketch pen
- Ruler
- Adhesive
Prerequisite Knowledge
- Square and its area.
- Rectangle and its area.
- Trapezium.
Theory
- For square and its area refer to Activity 3.
- For rectangle and its area refer to Activity 3.
- Trapezium is a quadrilateral whose two sides are parallel and two sides are non-parallel. In the trapezium ABCD, sides AB and CD are parallel while sides AD and BC are non-parallel.
- Area of trapezium =½ (Sum of parallel sides x Distance between parallel sides)
= ½ (AB + CD) x DE
Procedure
- Cut out a square WQRS of side a units from a coloured paper, (see Fig. 5.2)
- Cut out a square WXYZ of side b units (b < a) from another coloured paper, (see Fig. 5.3)
- Paste the smaller square WXYZ on the bigger square WQRS as shown in Fig. 5.4.
- Join the points Y and R using sketch pen. (see Fig. 5.4)
- Cut out the trapeziums XQRY and ZYRS from WQRS (see Fig. 5.5 and 5.6).
- Paste both trapeziums obtained in step 5th on the drawing sheet as shown in Fig. 5.7
Demonstration
From Fig. 5.2 and Fig. 5.3, we have Area of square WQRS = a²
Area of square WXYZ = b² Now, from Fig. 5.4, we have
Area of square WQRS – Area of square WXYZ = Area of trapezium XQRY + Area of trapezium ZYRS
=Area of rectangle XQZS [from Fig. 5.7]
= XS . SZ [∴ Area of rectangle = Length x Breadth]
So, a² – b² = (a + b) (a – b)
Here, area is in square units.
Observation
On actual measurement, we get
a =…….. , b = …….. ,
So, a² =…….. ,
b² = …….. ,
a + b = …….. ,
a-b = …….. ,
a² -b² = …….. ,
and (a + b)(a-b) = …….. ,
Flence, a² – b² = (a + b) (a – b)
Result
The algebraic identity a² – b² = (a + b) (a – b) has been verified.
Application
The identity (a² – b²) = (a + b)(a-b) can be used for
- calculating the difference of squares of two numbers.
- getting some products involving two numbers.
- simplification and factorization of algebraic expressions.
Viva Voce
Question 1:
Which algebraic identity should be used to evaluate 64² — 36²?
Answer:
a² – b² = (a + b) (a – b)
Question 2:
If the sides of a rectangle are (√3 + √2) units and (√3 – √2) units, then what will be its area?
Answer:
1 sq unit
Question 3:
Is the identity a² – b² = (a + b) (a – b), holds for all real values of a and b?
Answer:
Yes
Question 4:
Is a² – b² a monomial?
Answer:
No, a² – b² is a binomial because it has two terms.
Question 5:
Find the degree of an identity a² – b² = (a – b) (a + b).
Answer:
The degree of an identity is two.
Question 6:
Write the places where the algebraic identity a² – b² = (a – b) (a + b) is used.
Answer:
This identity is used in solving the quadratic equation, mensuration problem, factorisation of polynomial, etc.
Question 7:
The algebraic identity a² – b² = (a- b) (a + b) is true for only natural numbers.
Answer:
No, it is true for all real numbers.
Question 8:
If we take both negative variables, then their is any effect of algebraic identity.
Answer:
No,
We know a² – b² = (a + b) (a – b)
Suppose we take a = -a and b = -b,
then (-a)² – (-b)² = (-a – b) (-a + b)
=> a² – b² = (a – b) (a + b)
Question 9:
Is the algebraic identity a² – b² = (a + b) (a – b) also true, if any one of the variable in the given identity is zero?
Answer:
Yes, suppose b = 0, then
a² – 0² = (a + 0) (0 – 0)
=> a² = a², true.
Suggested Activity
Verify that (x² – y² ) = (x + y) (x – y) by taking x = 9 and y = 7.
Math LabsMath Labs with ActivityMath Lab ManualScience LabsScience Practical Skills
NCERT Class 9 Maths Lab Manual
- Determine Construct a Square Root Spiral Class 9 Experiment
- Determine Represent Some Irrational Numbers on the Number Line Class 9 Experiment
- Determine Verify the Algebraic Identity (a+b)² = a² + 2ab+b² Class 9 Experiment
- Determine Verify the Algebraic Identity (a-b)² = a²- 2ab+b² Class 9 Experiment
- Determine Verify the Algebraic Identity a² – b² = (a+b) (a-b) Class 9 Experiment
- Determine Verify the Algebraic Identity(a+b+c)² = a²+b²+c²+2ab+2bc+2ca Class 9 Experiment
- Determine Verify the Algebraic Identity (a+b)³ = a³+b³+ 3a²b + 3ab² Class 9 Experiment
- Determine Verify the Algebraic Identity (a – b)³ = a³ – b³ – 3ab (a – b) Class 9 Experiment
- Determine Verify the Algebraic Identity a³+b³ = (a+b) (a²-ab+b²) Class 9 Experiment
- Determine Verify the Algebraic Identity a³-b³ = (a-b) (a²+ab+b²) Class 9 Experiment
- Determine Verify that if Two Lines Intersect each Other Class 9 Experiment
- Determine Verify that the Sum of the Angles of a Triangle is 180° Class 9 Experiment
- Determine Verify Exterior Angle Property of a Triangle Class 9 Experiment
- Determine Verify the Different Criteria for Congruency of Triangles Class 9 Experiment
- Determine Verify that in a Triangle, Longer Side has the Greater Angle Class 9 Experiment
- Determine Find the Values of Abscissae Class 9 Experiment
- Determine Find a Hidden Picture by Plotting Class 9 Experiment