Class 08 Activity2 – Algebraic Expressions

Objective: 

To verify the identity (x-y)² = x² + y² – 2xy.

Materials Required: 

Some thick sheets of paper (cardboard), scissors, geometry box, sketch pen, pencil, etc.

Procedure: 

Let us verify the identity (x-y)² = x² + y² - 2xy by taking x = 6, y = 4.

1. On a thick sheet of paper (cardboard), draw a figure as shown below. This shape is a combination of two squares, one with side 6 cm and other with side 4 cm. Using scissors, cut it out. Area of this shape = (6² + 4²) cm²

2. From the above piece, cut out a rectangle of size 6 cm x 4 cm, marked as I in the figure. 

Area of piece I = (6 x 4) cm².

3. From the remaining shape, cut out a rectangle of size 6 cm x 4 cm, marked as II in the figure.

Area of piece II = (6 x 4) cm²

4.Finally, you are left with a square piece of side = (6 -4) cm = 2 cm Area of this shape = (6-4) x (6 – 4)= (6-4)² cm²

5. Area of the shape in fig. 1 = (6² +4²) cm² 

Area of the shape after cutting out I =  (6² + 4²) –  (6 x 4) 

Area of the shape after cutting out II  

= (6² + 4²) –  (6 x 4) - (6x4) 

= [6² + 4² – 2 x (6x4)] cm² 

But, after cutting out II, you are left with a square piece of

 area (6 - 4)² cm² 

Thus, (6-4)² = 6² + 4² – 2 x (6 x 4)

 (x-y)² = x² + y² – 2xy [Q x = 6, y = 4]

Do Yourself:

Verify the identity (x-y)² = x² + y² – 2xy for the following pairs of numbers:

(i) x = 3, y = 1 (ii) x = 5, y = 2

(iii) x = 7, y = 5 (iv) x = 8, y = 3