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Question

Evaluate the following using suitable identities:
(i)(99)3
(ii) (102)3
(iii) (998)3

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Solution

(i)(99)3

=(1001)3

We know that(ab)3=a3b33ab(ab) (1)

In this problem, we have a=100 and b=1, putting these values in (1), we get

(1001)3=(100)3(1)33(100)(1)(1001)=1000000129700=970299

(ii)(102)3

=(100+2)3

We know that (a+b)3=a3+b3+3ab(a+b) (1)

In this problem, we have a=100 and b=2, putting these values in (1), we get

(100+2)3=(100)3+(2)3+3(100)(2)(100+2)=1000000+8+61200=1061208

(iii)(998)3

=(1002)3

We know that (ab)3=a3b33ab(ab) (1)

In this problem, we have a=1000 and b=2, putting these values in (1), we get

(10002)3=(1000)3(2)33(1000)(2)(10002)=100000000085988000=994011992


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