Class 9 Exam > Class 9 Notes > Lab Manuals for Class 9 > Lab Manual: Algebraic Identity a^2 – b^2 = (a+b) (a-b)
Lab Manual: Algebraic Identity a^2 – b^2 = (a+b) (a-b) | Lab Manuals for Class 9 PDF Download
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.
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