Find the value of the following:
(a) $ 297 \times 17+297 \times 3 $
(b) $54279 \times 92 + 8 \times 54279$
(c) $81265 \times 169 – 81265 \times 69$
(d) $3845 \times 5 \times 782 + 769 \times 25 \times 218$

To do: 

We have to find the values of the given expressions.

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:

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

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

Therefore using Distributive property,

(a) $297\times17+297\times3=297\times(17+3)$

$=297\times20$

$=5940$

The value of $297\times17+297\times3$ is $5940$.

(b) $54279\times92+8\times54279=54279\times(92+8)$

$=54279\times100$

$=5427900$

The value of $54279\times92+8\times54279$ is $5427900$.

(c) $81265 \times 169-81265 \times 69=81265\times(169-69)$

$=81265\times100$

$=8126500$

The value of \( 81265 \times 169-81265 \times 69 \) is $8126500$.

(d) 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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