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What will be the value of the product $101 × 102$ ?

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10302

10502

10660

10550

answer is A.

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Detailed Solution

The given expression is,

101 × 102

To avoid a lengthy calculation, it is better to divide the three-digit number into its simplest form and then expand the bracket using the algebraic identity.

∴ 101 × 102 = 100 + 1 100 + 2

Apply the algebraic identity,

x + a x + b = x 2 + x a + b + a b

∴ 101 × 102 = 100 + 1 100 + 2 ⇒ 101 × 102 = 1002 + 100 1 + 2 + 1 × 2 ⇒ 101 × 102 = 10000 + 300 + 2 ⇒ 101 × 102 = 10302.

Therefore, the value of the product

101 × 102 = 10302.

Hence, option (1) is correct.

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