Class 08 Activity – Algebraic Expressions

 Activity – 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 for x = 5, y = 3

On a thick sheet of paper, draw two squares one with side 5 cm and another with 4.side 3 cm. Using scissors, cut them out.

2. On another thick sheet of paper, draw two rectangles each with dimensions5 cm x 3 cm. Using scissors, cut them out.

Activity – Algebraic Expressions

3. Now, arrange the four pieces in such a way that the resulting figure becomes a square as shown in the figure.

4. We see that the resulting figure is a square of side (5+3)cm.

Area of the resulting square  = (5 + 3)² cm²

Also, area of piece I = 5 cm x 5 cm = 5² cm² 

area of piece II = 3 cm x 3 cm = 3² cm²

area of piece III = 5 cm x 3 cm = (5 x 3) cm² and 

area of piece IV = 5 cm x 3 cm = (5 x 3) cm² 

Thus, area of the resulting piece = area of the four pieces.

 (5 + 3)² = 5² + 3² + (5 x 3) + (5 x 3)

(5 + 3)² = 5² + 3² + 2 x (5 x 3)

 (x + y)² = x² + y² + 2xy {Q x = 5, y = 3]

Do Yourself:

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

x = 4, y = 2 (ii) x = 3, y = 6

(iii) x = 5, y = 4 (iv) x = 7, y = 8