Evaluate the following using suitable identities:

${(998)}^{3}$ [2 MARKS]

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Solution

Formula: 1 Mark
Application: 1 Mark

${(998)}^{3} = {(1000 - 2)}^{3}$
Using the identity
${(x - y)}^{3} = x^{3} - y^{3} - 3 x y (x - y)$

$= {(1000)}^{3} - {(2)}^{3} - 3 (100) (2) (1000 - 2)$

$= 1000000000 - 8 - 600 (998)$

$= 1000000000 - 8 - 598800$

$= 1000000000 - 598808$

$= 999401192$

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