SOLUTION: Factor xy^3-16xyz^2

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Question 191770: Factor
xy^3-16xyz^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
xy%5E3-16xyz%5E2 Start with the given expression.


xy%28y%5E2-16z%5E2%29 Factor out the GCF xy



Now let's factor y%5E2-16z%5E2:

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y%5E2-16z%5E2 Start with the given expression.


%28y%29%5E2-16z%5E2 Rewrite y%5E2 as %28y%29%5E2.


%28y%29%5E2-%284z%29%5E2 Rewrite 16z%5E2 as %284z%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=y and B=4z.


So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:


A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.


%28y%29%5E2-%284z%29%5E2=%28y%2B4z%29%28y-4z%29 Plug in A=y and B=4z.


So this shows us that y%5E2-16z%5E2 factors to %28y%2B4z%29%28y-4z%29.


In other words y%5E2-16z%5E2=%28y%2B4z%29%28y-4z%29.


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So xy%5E3-16xyz%5E2 completely factors to xy%28y%2B4z%29%28y-4z%29