Math Labs with Activity – Verify the Identity (a+b)² = (a² + 2ab+b²)
To verify the identity (a+b)² = (a² + 2ab+b²)
- A piece of cardboard
- A sheet of glazed paper
- A sheet of white paper
- A pair of scissors
- A geometry box
We take distinct values of a and b.
Step 1: On the glazed paper construct a square of side ‘a’ units. Construct two rectangles, each having length ‘a’ units and breadth ‘b’ units. Construct a square of side ‘b’ units.
Step 2: Paste the sheet of white paper on the cardboard. Draw a square ABCD having each side (a+b) units.
Step 3: Cut the two squares and the two rectangles from the glazed paper and paste them on the white paper. Arrange these inside the square ABCD as shown in Figure 10.1.
Step 4: Record your observations.
Observations and Calculations
- Area of the square ABCD drawn on the white paper =(a+b)² square units.
- Area of the square having each side a units (drawn on the glazed paper) =a² square units.
Area of the square having each side b units (drawn on the glazed paper) =b² square units.
Area of each rectangle (drawn on the glazed paper) = (ab) square units.
∴ total area of the four quadrilaterals (drawn on the glazed paper)
=(a² +b² + ab + ab) square units = (a² + 2ab+b²) square units.
Now, the area of the square ABCD = sum of the areas of the four quadrilaterals.
∴ wehave, (a+b)² = (a² + 2ab+b²).
The identify (a+b)² = (a² + 2ab+b²) is verified.