Question

Which of the following shows the distributive property of multiplication over subtraction?
A. $x(y - z) = (x \times y) - (x \times z)$
B. $x(y - z) = (x \times y) - z$
C. $x \times ( - y) = ( - x) \times y$
D. \[x \times \left( {\dfrac{{ - 1}}{y}} \right) = ( - x) \times \left( {\dfrac{1}{y}} \right)\]

Answer 1

Hint:
We know that the distributive property of multiplication has two equations, one for addition and one for subtraction, we will consider the distributive property of multiplication over subtraction as per the question, then we will compare the equation with the choices given and the one which matches will be the final answer.

Complete step by step solution:
We know that the distributive property of multiplication has two equations, one for addition and one for subtraction
(1) The distributive property of multiplication over addition,
 $ \Rightarrow a \times (b + c) = (a \times b) + (a \times c)$ … (1)

(2) The distributive property of multiplication over subtraction,
 $ \Rightarrow a \times (b - c) = (a \times b) - (a \times c)$ … (2)
According to the question, we need to compare (2) with the choices,
Since, the variables are as x, y, and z in the choices,
Put \[a = x,b = y\] and \[c = z\] in (2), we get
 $ \Rightarrow x \times (y - z) = (x \times y) - (x \times z)$ … (3)
Hence, we can now clearly say that
Option A matches equation (3).

Hence, the final answer is A.

Note:
In these types of questions, we should remember that this is a single choice correct question, hence if we find our answer before checking all the MCQs, there is no need to check for all the choices given to us when we have already found our final answer. This would save us lots of time and extra efforts which would be useful for some other question which needs more time to be solved. As a result of this practice, we would be able to predict the correct answer faster and more efficiently.