Answer: To expand and simplify the expression (3x - 1)^4, we can use the binomial theorem or the distributive property multiple times. Let's perform the expansion:
(3x - 1)^4 = (3x - 1)(3x - 1)(3x - 1)(3x - 1)
Using the distributive property, we can find all the terms:
(3x - 1)^4 = (3x * 3x * 3x * 3x) - (3x * 3x * 3x * 1) - (3x * 3x * 1 * 3x) - (3x * 3x * 1 * 1) - (3x * 1 * 3x * 3x) + (3x * 1 * 3x * 1) + (3x * 1 * 1 * 3x) + (3x * 1 * 1 * 1) - (1 * 3x * 3x * 3x) + (1 * 3x * 3x * 1) + (1 * 3x * 1 * 3x) + (1 * 3x * 1 * 1) - (1 * 1 * 3x * 3x) + (1 * 1 * 3x * 1) + (1 * 1 * 1 * 3x) - (1 * 1 * 1 * 1)
Now, let's simplify each term:
(81x^4) - (27x^3) - (27x^3) - (9x^2) - (27x^3) + (9x^2) + (9x^2) - (3x) - (27x^3) + (9x^2) + (9x^2) - (3x) - (9x^2) + (3x) + (3x) - 1
Combining like terms:
81x^4 - 108x^3 - 54x^2 - 12x - 1
Now, let's look at the monomials listed:
-4x^3, -27x^3, -54x^3, -108x^3
From the result, we can see that the term -108x^3 is present. So, the correct monomial listed below that is a term in the result is:
-108x^3