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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, $117 \times 83=9711$.
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