SOLUTION: 8xy^4 + 27x^4y factor completely, if prime state

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Question 571038: 8xy^4 + 27x^4y factor completely, if prime state
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
8xy^4 + 27x^4y =

xy(8y^3 + 27x^3) =

We now use the sum of cubes to factor the binomial in the parentheses.

In the parentheses, we apply the formula

(a^3 + b^3) = (a + b)(a^2 - 2b + b^2)

Then (8y^3 + 27x^3) becomes (2y + 3x)(4y^2 - 6xy + b^2).

Final answer = xy(2y + 3x)(4y^2 - 6xy + b^2)