If q= 999, then the value of $q (q^{2} + 3 q + 3)$ is

999999

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99999

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999999999

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none of these

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Solution

The correct option is C 999999999
Given q=999
Then $q (q^{2} + 3 q + 3) = q (q^{2} + 4 q + 4 - q - 1) = q ((q + 2)^{2} - (q + 1))$
Put the value q=999
Then $999 ((999 + 2)^{2} - (999 + 1)) = 999 ((1001)^{2} - 1000) = 999 (1002001 - 1000) = 999 \times 1001001 = 999999999$

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