SOLUTION: Factorise each of the following as possible. 7x*xy - 28x*x*x*y*y*y

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Question 859417: Factorise each of the following as possible.
7x*xy - 28x*x*x*y*y*y
Answer by Awesom3guy(31) About Me  (Show Source):
You can put this solution on YOUR website!

You have:
7%2Ax%2Ax%2Ay+-+28%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay
There are two terms here:
%287%2Ax%2Ax%2Ay%29+-+%2828%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%29

You are looking for the biggest thing you can "extract" or factor out of both of these terms.
The first term is smaller so you start with it.
Can you factor 7 from it? Sure. That gives you
7%2A%28x%2Ax%2Ay%29.
You can also factor 7 from the second term. That gives you
7%2A%284%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%29

Common sense suggests that you can keep going as there are more x'es and y's to factor our in both of these terms. So let's try the biggest thing you can do. Can you factor out 7%2Ax%2Ax%2Ay from the first term? sure you can. it's all multiplying so you have:
%287%2Ax%2Ax%2Ay%29%2A1

But can you factor out 7*x*x*y from the second one?
For this you have to have at least one number that is a multiple of 7, two x'es and one y. Of course there is all of that there. What isn't factored stays, so the second term becomes:
%287%2Ax%2Ax%2Ay%29%2A%284%2Ax%2Ay%2Ay%29

Now you can't factor, as there is nothing left to factor in the first term. This is what you have:
%287%2Ax%2Ax%2Ay%29%2A%281%29+-+%287%2Ax%2Ax%2Ay%29%2A%284%2Ax%2Ay%2Ay%29

Notice that the part %287%2Ax%2Ax%2Ay%29 appears in both terms, and that's what we wanted. Now you factor that part out of both of the terms and multiply it with everything that isn't that term together, or %281+%2B+4%2Ax%2Ay%2Ay%29.

%287%2Ax%2Ax%2Ay%29%2A%281+%2B+4%2Ax%2Ay%2Ay%29
And you're done! This isn't so long, I just explained it thoroughly :)