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What will be the value of the cube $1033$ by using the algebraic identity?

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1092772

1072727

1092227

1092727

answer is D.

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Detailed Solution

The given cube is

1033 .

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.

∴ 1033 = 100 + 3 2

Apply the algebraic identity,

a + b 3 = a 3 + b 3 + 3 a b b + a

∴ 1033 = 100 + 3 2 ⇒ 1033 = 1003 + 33 + 3 × 100 × 3 × 100 + 3 ⇒ 1033 = 1000000 + 27 + 900103 ⇒ 1033 = 1000027 + 92700 ⇒ 1033 = 1092727.

Therefore, the value of the cube

1033 = 1092727.

Hence, option (4) is correct.

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