**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:** On the glazed paper construct a square of side ‘a’ units. Construct two rectangles, each having length ‘a’ units and breadth ‘b’ units. Construct a square of side ‘b’ units.

**Step 2:** Paste the sheet of white paper on the cardboard. Draw a square ABCD having each side (a+b) units.

**Step 3:** Cut the two squares and the two rectangles from the glazed paper and paste them on the white paper. Arrange these inside the square ABCD as shown in Figure 10.1.

**Step 4:** Record your observations.

**Observations and Calculations**

- Area of the square ABCD drawn on the white paper =(a+b)² square units.
- Area of the square having each side a units (drawn on the glazed paper) =a² square units.

Area of the square having each side b units (drawn on the glazed paper) =b² square units.

Area of each rectangle (drawn on the glazed paper) = (ab) square units.

∴ total area of the four quadrilaterals (drawn on the glazed paper)

=(a² +b² + ab + ab) square units = (a² + 2ab+b²) square units.

Now, the area of the square ABCD = sum of the areas of the four quadrilaterals.

∴ wehave, (a+b)² = (a² + 2ab+b²).

**Result**

The identify (a+b)² = (a² + 2ab+b²) is verified.

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