Math Labs with Activity – Verify the Identity (a-b)² = (a² – 2ab+b²)

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Math Labs with Activity – Verify the Identity (a-b)² = (a² – 2ab+b²)

OBJECTIVE

To verify the identity (a-b)² = (a² – 2ab+b²)

Materials Required

  1. A piece of cardboard
  2. A sheet of glazed paper
  3. A sheet of white paper
  4. A pair of scissors
  5. A geometry box

Procedure
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.
Math Labs with Activity - Verify the Identity (a-b)² = (a² - 2ab+b²) 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).

Result
The identity (a-b)² = (a² – 2ab+b²) is verified.

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