SOLUTION: Factor using the formula for the sum or difference of two cubes: 27y^4+8y Thanks for the help

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Question 182028This question is from textbook
: Factor using the formula for the sum or difference of two cubes:
27y^4+8y
Thanks for the help This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

27y%5E4%2B8y Start with the given expression


y%2827y%5E3%2B8%29 Factor out the GCF y


Now let's focus on the inner expression 27y%5E3%2B8


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27y%5E3%2B8 Start with the given expression.


%283y%29%5E3%2B%282%29%5E3 Rewrite 27y%5E3 as %283y%29%5E3. Rewrite 8 as %282%29%5E3.


%283y%2B2%29%28%283y%29%5E2-%283y%29%282%29%2B%282%29%5E2%29 Now factor by using the sum of cubes formula. Remember the sum of cubes formula is A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29


%283y%2B2%29%289y%5E2-6y%2B4%29 Multiply


So 27y%5E3%2B8 factors to %283y%2B2%29%289y%5E2-6y%2B4%29.

In other words, 27y%5E3%2B8=%283y%2B2%29%289y%5E2-6y%2B4%29

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So this means that y%2827y%5E3%2B8%29 factors to y%283y%2B2%29%289y%5E2-6y%2B4%29


Answer:
So 27y%5E4%2B8y completely factors to y%283y%2B2%29%289y%5E2-6y%2B4%29