Solve the following:$3845 \times 5 \times 782+769 \times 25 \times 218$

Given :

The given expression is $3845 \times 5 \times 782+769 \times 25 \times 218$.

To do :

We have to solve the given expression.

Solution :

Distributive Property:

The distributive property of multiplication states that when a factor is multiplied by the sum or difference of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition or subtraction operation.

This property is symbolically stated as:

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

$a (b-c) = a\times b - a\times c$

3845 can be written as,

$3845 = 769\times 5$

Therefore,

 $3845 \times 5 \times 782+769 \times 25 \times 218=769\times 5 \times 5 \times 782+769 \times 25 \times 218$

                                                   $=769\times 25(782+218)$

                                                   $=769\times 25\times 1000$

                                                  $= (800-31)\times 25 \times 1000$

                                                 $= (800 \times 25 - 31 \times 25) \times 1000$

                                                $= (20000-775)\times 1000$

                                                $= 1922500$.

Therefore, the value of  $3845 \times 5 \times 782+769 \times 25 \times 218$ is 1922500.

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Updated on: 10-Oct-2022

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