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06/07/2021 11:42 am
Topic starter
Evaluate the following using suitable identities:
(i) (99)3
(ii) (102)3
(iii) (998)3
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06/07/2021 11:45 am
(i) (99)3
We can write 99 as 100–1
Using identity, (x –y)3 = x3–y3–3xy(x–y)
(99)3 = (100–1)3
= (100)3–13–(3×100×1)(100–1)
= 1000000 –1–300(100 – 1)
= 1000000–1–30000+300
= 970299
(ii) (102)3
We can write 102 as 100+2
Using identity,(x + y)3 = x3+y3+3xy(x + y)
(100+2)3 =(100)3+23+(3×100×2)(100+2)
= 1000000 + 8 + 600(100 + 2)
= 1000000 + 8 + 60000 + 1200
= 1061208
(iii) (998)3
We can write 99 as 1000–2
Using identity, (x–y)3 = x3–y3–3xy(x–y)
(998)3 = (1000–2)3
=(1000)3–23–(3×1000×2)(1000–2)
= 1000000000–8–6000(1000– 2)
= 1000000000–8- 6000000+12000
= 994011992