Math Labs with Activity – Verify the Identity (a² – b²) = (a+b)(a-b) (Method 2)
To verify the identity (a² – b²) = (a+b)(a-b) (Method 2)
- 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
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).
The identity (a² – b²) = (a+b)(a-b) is verified geometrically.