3a²bc²(3a²-4b-c)

9a^4bc^2 - 12a^2b^2c - 3a^2bc

To simplify the expression 3a²bc²(3a²-4b-c), we can multiply each term inside the parentheses by each term outside the parentheses:

Step 1: Distribute 3a² over (3a²-4b-c)
3a² × 3a² = 9a⁴
3a² × -4b = -12a²b
3a² × -c = -3a²c

Step 2: Distribute bc² over (3a²-4b-c)
bc² × 3a² = 3a²bc²
bc² × -4b = -4b³c²
bc² × -c = -bc³

Now, we can combine like terms to simplify the expression:

9a⁴ - 12a²b - 3a²c + 3a²bc² - 4b³c² - bc³