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2.Evaluate the following products without multiplying directly
i)103 × 107
ii)95 × 96
iii)104 × 96
Answer :

i)103 × 107 = (100 + 3)(100 + 7)
Using identity (iv), i.e.,\((x + a)(x + b) = x^2 + (a + b)x + ab\)
We have, \((100 + 3)(100 + 7) = {100}^2 + (3 + 7)100 + (3)(7)\)
\(= 10000 + 1000 + 21\)
\(= 11021\)

ii)95 × 96 = (100 - 5)(100 - 4)
Using identity (iv), i.e.,\((x + a)(x + b) = x^2 + (a + b)x + ab\)
We have, \((100 - 5)(100 - 4) = {100}^2 - (5 + 4)100 + (4)(5)\)
\(= 10000 - 900 + 20\)
\(= 9120\)

iii)104 × 96 = (100 + 4)(100 - 4)
Using identity (iii), i.e.,\((a^2 - b^2) = (a + b)(a - b)\)
We have, \((100 + 4)(100 - 4) = {100}^2 - {4}^2\)
\(= 10000 - 16\)
\(= 9984\)