Explanation:
(i)
(81)^2
Use (a + b)^2 = a^2 + 2ab + b^2
(81)^2 = (80 + 1)^2 =
= 80^2 + 2 * 80 * 1 + 1^2
= 6400 + 160 + 1
= 6561
(ii)
(198)^2
Use (a - b)^2 = a^2 - 2ab + b^2
(198)^2 = (200 - 2)^2 =
= 200^2 - 2 * 200 * 2 + 2^2
= 40,000 - 800 + 4
= 39,204
(iii)
165 * 155
Use (a + b)(a - b) = a^2 - b^2
165 * 155 = (160 + 5)(160 - 5) =
= 160^2 - 5^2
= 25,600 - 25
= 25,575
(iv)
(7.25)^2 - (2.75)^2
Use a^2 - b^2 = (a + b)(a - b)
(7.25)^2 - (2.75)^2 =
= (7.25 + 2.75)(7.25 - 2.75)
= 10(4.5)
= 45