Question

Factor completely: 45x³y - 75x²y² - 30x⁴y³

a) 15x²y²(3x - 5y - 2x²y)
b) 5xy³(9x² - 15y - 6x³y²)
c) 15x²y²(3x + 5y - 2x²y)
d) 5xy³(9x² + 15y - 6x³y²)

Answer 1

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).