Question

The expression \[xy - xz\] is equivalent to:
A. \[x\left( {y - z} \right)\]
B. \[y\left( {z - x} \right)\]
C. \[x\left( {y + z} \right)\]
D. \[z\left( { - x + y} \right)\]

Answer 1

Hint: First of all, find the common variable between both the terms in the expression. Then separate the common variable using distributive property, \[a\left( {b + c} \right) = ab + ac\].

Complete step-by-step solution:
Here, we have to find an expression which is equivalent to \[xy - xz\].
As we can see that both terms \[xy\] and \[ - xz\] in the given expression have the \[x\] variable common between them.

We know that for any numbers or variables a, b, c, we have \[a\left( {b + c} \right) = ab + ac\]. This property is called distributive property.

In the first term \[x\] is multiplied with \[y\] and in the second term \[x\] is multiplied with \[ - z\]. Separate \[x\] from both the terms using distributive property, \[a\left( {b + c} \right) = ab + ac\].
\[xy - xz = x\left( {y - z} \right)\]

Therefore, the correct option is A.

Note: In this question, note that we can only take out the common variable and write it in multiplication with other terms of the expression. Try to use a suitable property which helps in taking out the common term from an expression.