Question

Evaluate using identity
99^3
1001^3

Answer 1

here is ur ans mate
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Answer 2

We know that:

( a - b )^3 = a^3 - b^3 - 3 a b ( a - b) .............................(1)

Using this formula we can solve any identities like this:

99 ^ 3

==> ( 100 - 1)^3

==> ( 100^3 - 1^3 -3*100*1(100 - 1)

==> 1000000 - 1 - 300*99

==>1000000-1-29700

==> 970299

Answer : 970299

Now we know that:

( a + b)^3 = a^3 + b^3 + 3 a b(a + b).......................................(2)

==> 1001^3

==>( 1000 + 1 )^3

==> 1000^3 + 1^3 +3*1000*1(1000+1)

==> 1000000000 + 1 + 3000* 1001

==> 1000000000 + 1 + 3003000

==> 1003003001

Answer : 1003003001

Hope it helps you

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