Final answer:
To factor completely the expression 45x³y - 75x²y² - 30x⁴y³, the greatest common factor of all the terms is 15x²y². By factoring out this common factor, we get 15x²y²(3x - 5y - 2x²y).
Step-by-step explanation:
To factor completely the expression 45x³y - 75x²y² - 30x⁴y³, we need to look for the greatest common factor of all the terms. In this case, we can see that the greatest common factor is 15x²y². By factoring out this common factor, we get:
45x³y - 75x²y² - 30x⁴y³ = 15x²y²(3x - 5y - 2x²y)
Therefore, the correct answer is option (a) 15x²y²(3x - 5y - 2x²y).