Question

Evaluate following using identities:

991 ☓ 1009

Answer 1

In the given problem, we have to evaluate expressions by using identities.

The given expression is 991 x 1009

We have `(991 + 1009)/2 = 1000`

So we can express 991 and  1009 in the terms of 1000 as

991 = 1000 - 9

1009 = 1000 + 9

`991 xx 1009 = (1000 - 9)(1000 + 9)`

We shall use the identity  `(x - y)(x + y) = x^2 - y^2`

Here

(x - y) = (1000 - 9)

(x + y) = (1000 + 9)

By applying in identity we get 

`(1000 - 9)(1000 + 9) = (1000)^2 - (9)^2`

= 1000000 - 81

= 999919

Hence the value of 991 x 1009 is 999919