SOLUTION: factor cube root 27x^3+125y^3

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Question 281327: factor cube root
27x^3+125y^3
Answer by dabanfield(803) (Show Source):
You can put this solution on YOUR website!
27x^3+125y^3
27x^3 = 3^3*x^3 = (3x)^3
125y^3 = 5^3*y^3 = (5y)^3
Using the fact that a^3 + b^3 = (a+b)*(a^2-ab+b^2) and substituting 3x for a and 5y for b we have:
(3x)^3 + (5y)^3 = (3x+3y)*((3x)^2-(3x*5y)+(5y)^2)) =
3*(x+y)*(9x^2 - 15xy + 25y^2)