Q3 of 59 Page 265

Verify the identity (a + b) (a – b) ≡ a2 – b2 geometrically by taking

a = 2 units, b = 1 unit

Refer the above figure.

Here a2-b2 = Area of figure I + Area of figure II = a(a-b) + b(a-b) = (a-b)(a + b)


Thus a2-b2 = (a-b)(a + b).


Here a = 2 units and b = 1 units


So, L.H.S = a2-b2 = 22-12 = 3 units


R.H.S = (a-b)(a + b) = (2-1)(2 + 1) = 3 units


Therefore L.H.S = R.H.S


Hence,the identity is verified.


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