Evaluate the following using suitable identities:-

(99)^{3}

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#### Solution

It is known that,

(a + b)^{3} = a^{3} + b^{3} + 3ab(a + b) and (a - b)^{3} = a^{3} - b^{3} - 3ab(a - b)

∴ (99)^{3 }= (100 − 1)^{3}

= (100)^{3} − (1)^{3} − 3(100)(1)(100 − 1)

= 1000000 − 1 − 300(99)

= 1000000 − 1 − 29700

= 970299

Concept: Algebraic Identities

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