Question

RHS part of the equation \[36(8 - 3) = \_\_\_\_\_\_\]
A. \[38 - 36\]
B.\[(36 \times 8) \times (36 - 3)\]
C.\[(36 \times 8) - (36 \times 3)\]
D.\[(36 \times 8) - 3\]

Answer 1

Hint: We use the distributive property of multiplication over subtraction \[a \times (b - c) = a \times b - a \times c\] to open the term and write RHS.
* Distributive property is the property that helps to break the multiplication of large numbers into the sum of multiplication of smaller numbers. We distribute the large number into two or more parts and then multiply the number outside the bracket to each of the distributed parts.

Complete step by step answer:
We know distributive property of multiplication over subtraction is given by\[a \times (b - c) = a \times b - a \times c\]
We have to use distributive property on the term \[36 \times (8 - 3)\] … (1)
Comparing the values from equation (1) to general equation \[a \times (b - c) = a \times b - a \times c\]
\[a = 36,b = 8,c = 3\]
Substituting values in RHS of general form
\[ \Rightarrow 36 \times (8 - 3) = (36 \times 8) - (36 \times 3)\]
So, the RHS of the equation given in the question is \[(36 \times 8) - (36 \times 3)\]

Therefore, option C is correct.

Additional Information:
The distributive property is helpful in solving the algebraic expressions as they make the solution easier when complex and large algebraic terms are distributed in a simpler form.
Example: \[4{x^2}(1005x) = 4{x^2} \times (1000x + 5x)\]
Using the distributive property we can write
\[ \Rightarrow 4{x^2}(1005x) = 4{x^2} \times 1000x + 4{x^2} \times 5x\]
Doing multiplication of separate terms on RHS
\[ \Rightarrow 4{x^2}(1005x) = 4000{x^3} + 20{x^3}\]
Add the terms in RHS
\[ \Rightarrow 4{x^2}(1005x) = 4020{x^3}\]

Note:
Students might try to solve the term inside the bracket first as it will give a smaller number to be multiplied by the first term, but since we do not have an option to choose a final value we find the possible solution using distributive property.
Also, many students might choose the second option in a rush as it is broken down into two brackets, so they might think that it is broken using distributive property, but here we have to have subtraction in between the terms that are being distributed.