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# 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. $z\left( { - x + y} \right)$

Last updated date: 14th Aug 2024
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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.