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Question
Evaluate the following product without multiplying directly:
103 × 107
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Solution
103 × 107 = (100 + 3) (100 + 7)
= (100)2 + (3 + 7) 100 + (3) (7)
By using the identity (x + a)(x + b) = x2 + (a + b)x + ab,
where x = 100, a = 3, and b = 7
= 10000 + 1000 + 21
= 11021
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