Class 08 Activity – Algebraic Expressions3

Objective: 

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

Materials Required: 

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

 Procedure: 

Let us verify the identity x²-y² = (x + y) (x-y) by taking r = 7, y = 4.

On a thick sheet of paper (cardboard), draw a square of side 7 cm. Cut it out.

Area of this piece = 7 x 7 cm² = 7² cm²

2. From one of its corners, cut out a square piece of side 4 cm, as shown in the figure.

Area of the remaining shape = (7² – 4²) cm²

3. Now, cut the remaining shape along the dotted line and rearrange the two rectangles as shown. 

Clearly, the resulting figure is a rectangle of dimensions (7 + 4) cm x (7-4) cm. So, area of this shape = (7 + 4) x (7-4) cm².

But, this-rectangular piece is rearrangement of the piece of area  (7² – 4²) cm²

 [ step 2]

Thus (7² – 4²) = ( 7 + 4) x ( 7-4)cm²

x²- y² = (x + y) (x-y). [ x =7, y=4]

Do Yourself:

Verify the identity, x²-y² = (x + y) (x-y) using the following pairs of numbers:

X = 4, y=3

(ii) X = 6, y = 2

(iii) x= 8, y = 4

(iv) X = 7, y=2

(v) x=10, y=4

(vi) X =9, y =6