SOLUTION: Factor using the formula for the sum or difference of two cubes: 54-16y^3 Thanks for the help

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Question 182026This question is from textbook
: Factor using the formula for the sum or difference of two cubes:
54-16y^3
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!

54-16y%5E3 Start with the given expression


2%2827-8y%5E3%29 Factor out the GCF 2


Now let's focus on the inner expression 27-8y%5E3


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27-8y%5E3 Start with the given expression.


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


%283-2y%29%28%283%29%5E2%2B%283%29%282y%29%2B%282y%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


%283-2y%29%289%2B6y%2B4y%5E2%29 Multiply


So 27-8y%5E3 factors to %283-2y%29%289%2B6y%2B4y%5E2%29.


In other words, 27-8y%5E3=%283-2y%29%289%2B6y%2B4y%5E2%29


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So 2%2827-8y%5E3%29 factors further to 2%283-2y%29%289%2B6y%2B4y%5E2%29



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Answer:
So 54-16y%5E3 completely factors to 2%283-2y%29%289%2B6y%2B4y%5E2%29