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The expression (3x - 1)4 is expanded and simplified. Which monomial listed below is a term in the result? -4 x3 -27 x3 -54 x3 -108 x3

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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

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