Completely factor nine 𝑥𝑚 minus three 𝑥 squared plus six 𝑚𝑦 minus two 𝑥𝑦.
Here we can factor by grouping. So we need to begin by grouping the first two terms together and grouping the last two terms together. And now, out of both sets of parentheses, we need to take out a greatest common factor.
Out of nine 𝑥𝑚 minus three 𝑥 squared, we can take out a three 𝑥. And after taking it out of both terms, we’re left with a three 𝑚 minus 𝑥. For our next pair of parentheses, we can take out a two 𝑦 as the greatest common factor. And after doing so, we are left with three 𝑚 minus 𝑥.
So the greatest common factors come together to be one factor. And the matching parentheses come together to be a factor. So our final answer is three 𝑥 plus two 𝑦 times three 𝑚 minus 𝑥.