Question

Evaluate the following using identities:

117 x 83

Answer 1

The given expression is  117 x 83

We have

`(117 + 83)/2 = 200/2`

= 100

So we can express 117 and 83 in the terms of 100 as

117 = 100 + 17

83 = 100 - 17

117 x 83 = (100 + 17)(100 - 17)

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

Here

(x + y) = 100 + 17

(x - y) = 100 - 17

By applying in identity we get 

`(100 + 17)(100 - 17) = (100)^2 - (17)^2`

= 10000 - 289

= 9711

Hence the value of 1117 x 83 is 9711