Evaluate the following using identities:
(a) $1007 \times 1004$
(b) $121^{2}-31^{2}$

Given:

The given expressions are (a) $1007 \times 1004$ and (b)  $121^{2}-31^{2}$.

To do :

We have to evaluate the given expressions using identities.

Solution :

 (a) $1007 \times 1004$

We know that,

$(a+b) \times (c+d) = a \times (c+d) + b \times (c+d)$

Therefore,

$1007 \times 1004 = (1000+7) \times (1000+4)$

                       $ = 1000  \times  1000 + 1000  \times  4 + 7  \times  1000 + 7  \times  4$

                        $= 1000000 + 4000 + 7000 + 28$

                       $ = 1011028$.

The value of $1007 \times 1004$ is $1011028$.

(b)  $121^{2}-31^{2}$

We know that,

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

Therefore,

 $121^{2}-31^{2} = (121+31)(121-31)$

                     $= (152)(90)$

                     $= 13680$

The value of $121^{2}-31^{2}$ is $13680$.

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Updated on: 10-Oct-2022

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