Evaluate the following by using identities:
(i) $98^{3}$

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Solution

We know that,
${(a - b)}^{3} = a^{3} - b^{3} - 3 a^{2} b + 3 {a b}^{2}$
$= a^{3} - b^{3} - 3 a b (a - b)$
${(a + b)}^{3} = a^{3} + b^{3} + 3 a b (a + b)$

Now we will use the above two identities to compute the cube of big numbers.

$98^{3} = {(100 - 2)}^{3} = {(100)}^{3} - 8 - 3 \times 100 \times 2 (100 - 2)$
$= 10, 00, 000 - 8 - 600 \times 98$
$= 10, 00, 000 - 8 - 58, 800$
$= 9, 41, 192$

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Similar questions

Evaluate the following using suitable identities:
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