Evaluate the following without actual multiplication:- $105\times 98$

Given :

The given expression is $105\times 98$

To do :

We have to evaluate the given expression without actual multiplication.

Solution :
 

$105\times 98$

$105\times 98 = (100+5)\times (100-2)$

We know that, 

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

Here, $x = 100, a = 5, b = 2$

So, $ (100+5)\times (100-2) = 100^2 + 100(5-2) - 5 \times 2$

                                                $ = 10000 + 100 (3) - 10$

                                                $ = 10000 + 300 - 10$

                                                $ = 10000 + 290$

                                              $ = 10290$

Therefore, the value of $105\times 98$ is $10290$.

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Updated on: 10-Oct-2022

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