Evaluate each of the following using identities:$117 \times 83$

Given:

$117 \times 83$

To do:

We have to evaluate the given expression using a suitable identity.

Solution:

We know that,

$(a+b)^2=a^2+b^2+2ab$

$(a-b)^2=a^2+b^2-2ab$

$(a+b)(a-b)=a^2-b^2$

Therefore,

$117 \times 83=(100+17)(100-17)$

$=(100)^{2}-(17)^{2}$

$=10000-289$

$=9711$

Hence, $117 \times 83=9711$.