SOLUTION: Factor: 2x^3-54y^3. (You will need to use the formula for a difference of cubes)

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Question 200130: Factor: 2x^3-54y^3. (You will need to use the formula for a difference of cubes)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E3-54y%5E3 Start with the given expression


2%28x%5E3-27y%5E3%29 Factor out the GCF 2


Now let's focus on the inner expression x%5E3-27y%5E3

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x%5E3-27y%5E3 Start with the given expression.


%28x%29%5E3-%283y%29%5E3 Rewrite x%5E3 as %28x%29%5E3. Rewrite 27y%5E3 as %283y%29%5E3.


%28x-3y%29%28%28x%29%5E2%2B%28x%29%283y%29%2B%283y%29%5E2%29 Now factor by using the difference of cubes formula.


Remember the difference of cubes formula is A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29



%28x-3y%29%28x%5E2%2B3xy%2B9y%5E2%29 Multiply


So x%5E3-27y%5E3 factors to %28x-3y%29%28x%5E2%2B3xy%2B9y%5E2%29.

In other words, x%5E3-27y%5E3=%28x-3y%29%28x%5E2%2B3xy%2B9y%5E2%29


So 2%28x%5E3-27y%5E3%29 factors further to 2%28x-3y%29%28x%5E2%2B3xy%2B9y%5E2%29


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Answer:


So 2x%5E3-54y%5E3 completely factors to 2%28x-3y%29%28x%5E2%2B3xy%2B9y%5E2%29


In other words, 2x%5E3-54y%5E3=2%2A%28x-3y%29%2A%28x%5E2%2B3xy%2B9y%5E2%29