Completely factor four 𝑧 squared 𝑥 minus 𝑧𝑥 squared plus four 𝑛𝑧 minus 𝑛𝑥.
Here, we can factor by grouping. And we do so by grouping the first two terms together and the last two terms together. And now, we take out a greatest common factor from each set of parentheses. We can take out a 𝑧 and an 𝑥 from the first set. And if we would take out 𝑧 and 𝑥 from both of these terms, we would be left with four 𝑧 minus 𝑥.
And out of the last two terms, we can take out an 𝑛. So the 𝑛 is our GCF — our greatest common factor. And once we take that out, we are left with four 𝑧 minus 𝑥. So the greatest common factors come together to be one factor. And then these matching terms become another factor.
So our final answer is 𝑧𝑥 plus 𝑛 times four 𝑧 minus 𝑥.