Question

Factorize \[z-7+7xy-xyz\].

Answer 1

Hint: To solve this question we first take the common out of the equation in such a way that both brackets left after taking the common part out will be the same. In that way we can then factorise the remaining terms to get the answer in this question.

Complete step-by-step answer:
The equation we need to factorize here is
\[z-7+7xy-xyz\]
In this equation we can see that there are three different variables now we must try taking something common out of two terms on both sides so that we can factorize them. Therefore we start by taking 2 terms at a time to rationalize this equation easily.
Now first we take the first two terms as we can see that there is nothing similar in both of them except the fact that both of these terms are divisible by one. Therefore we can take one out of both terms and write this equation now as
\[1\left( z-7 \right)+7xy-xyz\]
Now we take the third and fourth term in question and check what is common in both terms that they are multiplied by. Now as we can see in both terms \[xy\] is a common variable. Therefore we can take that out of both terms and write it as
\[1\left( z-7 \right)+xy\left( 7-z \right)\]
Now as we can see the equation which had four terms to begin with has now reduced to two terms but since both brackets in the terms aren’t common we can’t take anything common.
To make both the brackets same we take negative sign out of the bracket giving us
\[1\left( z-7 \right)-xy\left( z-7 \right)\]
Now since in both terms the bracket is common taking \[z-7\] common from both terms we get
\[\left( 1-xy \right)\left( z-7 \right)\]
This is the factored form of the question
So, the correct answer is “\[\left( 1-xy \right)\left( z-7 \right)\]”.

Note: An alternative to solving this question is by first taking \[-7\] common from second and third term and then taking z common from first and fourth giving us the same answer.
To explain this in small steps
\[z-7+7xy-xyz\]
\[-7+7xy+z-xyz\]
\[-7\left( 1-xy \right)+z\left( 1-xy \right)\]
\[\left( 1-xy \right)\left( z-7 \right)\]