Question

Evaluate the following using suitable identities
i. (99)³
ii. (102)³
​

Answer 1

Answer:

Step-by-step explanation:

We have,

(99)  

3

 

=(100−1)  

3

 

 

We know that

(a−b)  

3

=a  

3

−b  

3

−3ab(a−b)

 

Therefore,

=(100)  

3

−1  

3

−3×100×1×(100−1)

=1000000−1−300(100−1)

=1000000−1−30000+300

=970299

 

Hence, this is the answer.

Let us rewrite (102)  

3

 as (100+2)  

3

 

Now using the identity (a+b)  

3

=a  

3

+b  

3

+3ab(a+b), we get

(100+2)  

3

=100  

3

+2  

3

+[(3×100×2)(100+2)]

=1000000+8+(600×102)

=1000000+8+61200

=1061208

Hence, (102)  

3

=1061208