Question

Evaluate the following using suitable identities:

a) (99)^3
b) (102)^3
c) (998) ^3
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Answer 1

Answer:

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(i) (99)³

Solution:

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

Solution:

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

Solution:

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

Answer 2

Answer:

very good writing

but I am in 12th

not 9th

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