Final answer:
The coefficient of the x² term in the expansion of (3x² - 2)³ is 36, calculated by taking the second term of the binomial expansion and combining the coefficients.
Step-by-step explanation:
The question asks for the coefficient of the x² term when the expression (3x² - 2)³ is expanded and simplified. To find this, we can use the binomial theorem or expand it manually. When using binomial expansion, we only need to look at the terms that will result in an x² term when cubed. The relevant term in the expansion is the second term of the binomial expansion, which is 3 (the binomial coefficient from (3 choose 1)) multiplied by the first term once (which is 3x²) and the second term squared (which is -2 squared).
So the coefficient for the x² term is given by:
3 * (3x²) * (-2)² = 3 * 3x² * 4 = 36x²
The coefficient of the x² term after expanding and simplifying is 36.