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Last updated date: 18th Jun 2024
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Answer
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Hint: Distributive property which means the distribution of multiplication over addition can be used here since the two arithmetic operations addition and multiplication are present here. So by using the distributive property of real numbers we can simplify the above expression easily.

Complete step-by-step solution:
Given
$4\left( {6x + 11} \right)..................................\left( i \right)$
Now in order to simplify equation (i) we have to use the distributive property of real numbers.
Distributive property:
In simple words distributive property simply means the distribution of multiplication over addition.
Such that if we apply distributive property to $a\left( {b + c} \right)$we get:
$a\left( {b + c} \right) = ab + ac..........................\left( {ii} \right)$
Now on comparing we can see that $4\left( {6x + 11} \right)$is of the form $a\left( {b + c} \right)$such that we can directly apply the distributive property on$4\left( {6x + 11} \right)$.
So on applying the distributive property on$4\left( {6x + 11} \right)$, what we are really doing is distributing the number 4 over the terms of addition.
Such that on distributing 4 by multiplication we can write:
$4\left( {6x + 11} \right) = 4\left( {6x} \right) + 4\left( {11} \right).........................\left( {iii} \right)$
Now on simplifying (iii) we can write the final answer:
$
  4\left( {6x + 11} \right) = 4\left( {6x} \right) + 4\left( {11} \right) \\
   = 24x + 44..............................\left( {iv} \right) \\
 $
Therefore on simplifying $4\left( {6x + 11} \right)$we get$24x + 44$.

Additional Information:Distributive property has a wide range of applications and can be used to simplify problems having unlike terms inside a parenthesis or a bracket.

Note: Distributive properties are used in the cases where the terms inside a parentheses are not like terms and thus cannot be added to get the answer as such in like terms. Also while applying the distributive property it should be made sure that all the terms inside the bracket or parenthesis have been multiplied with the term outside the parentheses.