If $p = 99$ , then value of $p (p^{2} + 3 p + 3)$ is

1000

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99999

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100089

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999999

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Solution

The correct option is B $999999$
$p = 99$ (given)
$∴ p (p^{2} + 3 p + 3)$
$= p^{3} + 3 p^{2} + 3 p + 1 - 1 = (p + 1)^{3} - 1 = (99 + 1)^{3} - 1$
$= (100)^{3} - 1 = 1000000 - 1 = 999999$ .

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