Question

Evaluate the following by using identities:
(i) 98 (ii) 1001

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Answer 1

Answer:

(100-2)^2

100^2+2^2-2(100)(2)

10000+4-400

10000-396

=9604

(1000+1)^2

1000^2+1^2+2(1000)(1)

1000000+1+2000

1000000+20001

979999

Answer 2

Answer:

(i)98=

9604

(ii)1001=1002001

Step-by-step explanation:

(i)   We can write (98)² as ( 100 - 2)²

we know that (a-b)²=a²+2(ab)-b²

So, (100-2)² = (100)² +  2(100)(2)  - 2²

= 10000 + 400 - 4

Which is equal to

=10004-400 = 9604

• Therefore 98² = 9604

(ii)  we can write (1001)² as (1000+1)²

we know that (a+b)²=a²+2(ab)+b²

So,(1000+1)²=1000²+2(1000)(1)+1²

=1000000+2000+1

=1002001

• Therefore 1001²=1002001

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