SOLUTION: if 3x+2y=12 and xy=6 then what is 27x^3+8y^3

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Question 989965: if 3x+2y=12 and xy=6 then what is 27x^3+8y^3
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
27x%5E3%2B8y%5E3=%283x%2B2y%29%289x%5E2-6xy%2B4y%5E2%29
You can also show that,
%283x%2B2y%29%5E2=9x%5E2%2B12xy%2B4y%5E2
%283x%2B2y%29%5E2-18xy=9x%5E2-6xy%2B4y%5E2
So then,
27x%5E3%2B8y%5E3=%283x%2B2y%29%28%283x%2B2y%29%5E2-18xy%29
Substituting,
27x%5E3%2B8y%5E3=%2812%29%28%2812%29%5E2-18%286%29%29
27x%5E3%2B8y%5E3=%2812%29%28144-108%29
27x%5E3%2B8y%5E3=432