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

**OBJECTIVE**

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

**Materials Required**

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

**Procedure**

We take any values of a and b such that a>b.

**Step 1:** Construct a square ABCD on the glazed paper such that each side of this square measures a units. Inside this square construct another square AEFG of side b units (where b < a) as shown in Figure 9.1. Join FC.

**Step 2:** Paste the sheet of white paper on the cardboard. Cut the two quadrilaterals EBCF and GFCD from the glazed paper and place them on the white sheet.

**Step 3:** Reverse the quadrilateral GFCD. Now paste the two quadrilaterals on the sheet of white paper to obtain the rectangle EBGD.

**Observations and Calculations**

- In Figure 9.1, we have

area of square ABCD = a² square units

and area of smaller square AEFG =b² square units.

∴ area of quad. EBCF + area of quad. GFCD = area of square ABCD – area of square AEFG =(a² -b²) square units. - In Figure 9.3, we have

area of rect. EBGD = (a+b)(a-b) square units.

∴ area of quad. EBCF + area of quad. GFCD =(a+b)(a-b) square units.

Thus, from the above calculations we have (a² – b²) = (a+b)(a-b).

**Result**

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

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