Question

What is everything that could be equivalent to ((6x³ y⁹) * (7xy²)) - ((9x³ y²) * (3xy⁹) + (8xy²)²)?

A. 42x⁴ y¹1 - 27x⁶ y¹1 - 64x² y⁴
B. 42x⁴ y¹1 - 27x⁶ y¹1 + 64x² y⁴
C. 42x³ y⁹ - 27x³ y⁹ - 64x² y⁴
D. 42x⁴ y⁹ - 27x³ y⁹ - 64x² y⁴

Answer 1

To solve the given expression, simplify each term separately and then combine them to get 42x⁴ y¹¹ - 27x⁶ y¹¹ - 64x² y⁴.

Step-by-step explanation:

To solve the given expression, we need to simplify each term separately and then combine them.

First, simplify the first term: ((6x³ y⁹) * (7xy²)) = (6 * 7) * (x³ * x * y⁹ * y²) = 42x⁴ y¹¹.

Next, simplify the second term: ((9x³ y²) * (3xy⁹)) = (9 * 3) * (x³ * x * y² * y⁹) = 27x⁶ y¹¹.

Finally, simplify the third term: (8xy²)² = (8 * 8) * (x² * y²) = 64x² y⁴.

Now, substitute these simplified terms back into the original expression: 42x⁴ y¹¹ - 27x⁶ y¹¹ - 64x² y⁴.

Therefore, the correct option is A. 42x⁴ y¹¹ - 27x⁶ y¹¹ - 64x² y⁴.