How would you factor xz-4x+yz-4y?

Question

I tried to factor this equation but I'm not sure I did it right

Answer 1

What we want to do here is first check to see if the problem is organized where terms that have common factors are together. This problem meets that criteria because the first 2 terms have x and the 3rd and 4th terms have y in them.

Next, we write what both have in common first, so

x

You then divide x out of everything that has an x in it and write is as follows

x (z - 4)

Now we look at the 2nd part. We write the y since they both have y and divide y out of everything so

x (z - 4) + y (z -4)

Finally, if both sets of parenthesis have the same answers, we can combine the parts in front of the parenthesis as follows

(x + y) (z - 4)

And that's it! This is called factoring by grouping.