Question

Evaluate the following using suitable identities {1=99³}​

Answer 1

We have,

(99)3

=(100−1)3

 

We know that

(a−b)3=a3−b3−3ab(a−b)

 

Therefore,

=(100)3−13−3×100×1×(100−1)

=1000000−1−300(100−1)

=1000000−1−30000+300

=970299

 

Answer 2

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Step-by-step explanation:

We write 99 = 100 - 1; (99) ^ 3 = (100 - 1) ^ 3 Using (a - b) ^ 3 = a ^ 3 - b ^ 3 - 3ab * (a - b) Where a=100 8 b=1; =(100)^ 3 -(1)^ 3 -3(100) (1) (100 - 1); =1000000-1* 300(99) =1000000-1-2 29700 =970299