Final answer:
To factor the equation completely, we can start by factoring out the greatest common factors among the terms, and then continue factoring the expression inside the parentheses.
Step-by-step explanation:
To factor the equation completely, we need to look for the greatest common factors among the terms. In this case, the terms have common factors of 2, x, and y. Factoring out 2xy from each term gives us:
2xy(16x³+12x²y-4xy²-3y³)
Next, we can factor the expression inside the parentheses. We look for the greatest common factor among the terms, which is 4x³. Factoring out 4x³ gives us:
2xy(4x³(4+3xy-y²))
Finally, we can simplify the expression inside the parentheses further by grouping like terms:
2xy(4x³(3xy-y²+4))
Therefore, the completely factored form of the equation is 2xy(4x³(3xy-y²+4)).