Lab Manual: Verify the Algebraic Identity (a - b)² = a²- 2ab + b² | Lab Manuals for Class 9 PDF Download

Objective

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.