Evaluate each of the following using identities:$991 \times 1009$

Given:

$991 \times 1009$

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,

$991 \times 1009=(1000-9)(1000+9)$

$=(1000)^{2}-(9)^{2}$

$= 1000000-81$

$=999919$

Hence, $991 \times 1009=999919$.

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Updated on: 10-Oct-2022

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