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: Paste the white paper on the cardboard. Draw a square ABCD of side a units.
Step 2: Calculate the value of (a – b). On the glazed paper, construct two rectangles each having length (a-b) units and breadth b units. Also, construct a square of side b units.
Step 3: Cut the square and the two rectangles from the glazed paper and place them on the white paper. Arrange these inside the square ABCD as shown in Figure 11.1.
Step 4: Label the diagram as shown in Figure 11.1. Record your observations.
Observations and Calculations
We observe that the area of square AEFH=(a-b)² square units.
Also, area of square AEFH
= area of square ABCD – area of rect. EBGF – area of rect. HFID – area of square FGCI
i. e., (a-b)² = a²-(a-b)b-(a-b)b-b²
=> (a-b)² =a²-ab+b²-ab+b²-b²
=> (a-b)² = (a² – 2ab+b²).
The identity (a-b)² = (a² – 2ab+b²) is verified.