Final answer:
The third term in the expanded form of (x - 2)^6 using the Binomial Theorem is -160x^3, which is not listed among the provided options, indicating an error in the question or the answer choices.
The correct option is not given.
Step-by-step explanation:
The student is asking to find the third term in the expanded form of the binomial (x - 2)^6 using the Binomial Theorem. The Binomial Theorem states that the expansion of (a + b)^n includes terms of the form C(n, k) * a^(n-k) * b^k, where C(n, k) is the binomial coefficient. For the third term of the expansion, k would be 2, as indexing begins at 0 for the first term.
To calculate the third term, we use the coefficients from the binomial expansion which follows the pattern C(n, k) = n!/(k!(n-k)!). Thus, the third term can be found using:
C(6, 2) * x^(6-2) * (-2)^2 = 15 * x^4 * 4 = 60x^4.
However, this is not the third term we are looking for since we begin counting from the term with x^6 as the first term. The actual third term is instead:
C(6, 3) * x^(6-3) * (-2)^3 = 20 * x^3 * (-8) = -160x^3.
The third term in the expanded form of (x - 2)^6 is -160x^3, which is not one of the provided options hence there might be an error in the question or the provided options.
The correct option is not given.