SOLUTION: I'm needing some help with the following problem: Factor each completely. Some may require several steps. y^3-8z^3 thanks!

Algebra ->  Equations -> SOLUTION: I'm needing some help with the following problem: Factor each completely. Some may require several steps. y^3-8z^3 thanks!      Log On


   

Question 186370: I'm needing some help with the following problem: Factor each completely. Some may require several steps.
y^3-8z^3
thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

y%5E3-8z%5E3 Start with the given expression.


%28y%29%5E3-%282z%29%5E3 Rewrite y%5E3 as %28y%29%5E3. Rewrite 8z%5E3 as %282z%29%5E3.


%28y-2z%29%28%28y%29%5E2%2B%28y%29%282z%29%2B%282z%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


%28y-2z%29%28y%5E2%2B2yz%2B4z%5E2%29 Multiply

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Answer:

So y%5E3-8z%5E3 factors to %28y-2z%29%28y%5E2%2B2yz%2B4z%5E2%29.


In other words, y%5E3-8z%5E3=%28y-2z%29%28y%5E2%2B2yz%2B4z%5E2%29