**Math Labs with Activity – Verify the Identity (a² – b²) = (a+b)(a-b) (Method 1)**

**OBJECTIVE**

To verify the identity (a² – b²) = (a+b)(a-b) (Method 1)

**Materials Required**

- A piece of cardboard
- A sheet of white paper
- A geometry box
- A tube of glue
- A coloured glazed paper
- A pair of scissors

**Procedure**

We shall verify the identity for a = 10, b = 3.

**Step 1:** Paste the white paper on the cardboard. Draw a rectangle ABCD of length AB = 13 cm and breadth BC = 10 cm on this paper as shown in Figure 8.1.

**Step 2:** Cut a rectangle EFGH of length EF = 10 cm and breadth FG = 3 cm from the coloured glazed paper as shown in Figure 8.2(a). Also, cut a square PQRS of side 3 cm as shown in Figure 8.2(b).

**Step 3:** Paste the rectangle EFGH over the rectangle ABCD such that the side EH falls on the side AD and the point H falls on the point D as shown in Figure 8.3.

**Step 4:** Paste the square PQRS over the rectangle ABCD such that the side QR falls on the side BC and the point R falls on the point C as shown in Figure 8.3.

**Step 5:** Produce the line GF to meet the side AB at a point M as shown in Figure 8.3.

**Observations and Calculations**

- Area of rectangle ABQE = (a+b)(a- b).
- Area of rectangle ABCD =(a+b)a.

Area of rectangle EFGH = ab.

Area of square PQRS = b².

area of rect. ABQE = (area of rect. ABCD) – (area of rect. EFGH) – (area of square PQRS) =(a+b)a-ab-b² = a² + ab-ab -b² = a²-b². - Equating the two values of the area of rectangle ABQE, we get

(a² – b²) = (a+b)(a-b).

**Result**

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

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