**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**

- A piece of cardboard
- A sheet of glazed paper
- A sheet of white paper
- A pair of scissors
- 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.

**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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