Question 8 of 43beginner🔧 ApplyNumerical3 marks

Find the values of the following using the identity (a - b)^2 = a2a^{2} - 2ab + b2b^{2}.

(i)

(79)^2

Answer

Using the identity (a - b)^2 = a2a^{2} - 2ab + b2b^{2}, let a = 80 and b = 1.

(79)^2 = (80 - 1)^2 = (80)^2 - 2(80)(1) + (1)^2 = 6400 - 160 + 1 = 6241

(ii)

(193)^2

Answer

Let a = 200 and b = 7.

(193)^2 = (200 - 7)^2 = (200)^2 - 2(200)(7) + (7)^2 = 40000 - 2800 + 49 = 37249

(iii)

(299)^2

Answer

Let a = 300 and b = 1.

(299)^2 = (300 - 1)^2 = (300)^2 - 2(300)(1) + (1)^2 = 90000 - 600 + 1 = 89401

Explanation

The identity (a - b)^2 = a2a^{2} - 2ab + b2b^{2} is highly effective for finding the squares of numbers that are slightly less than a round number (like multiples of 10 or 100). By expressing the given number as (a - b), where 'a' is the nearest round number and 'b' is the small difference, the calculation simplifies into basic arithmetic operations that are easy to compute mentally or on paper.

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