(3a - 2b) ^ 2 =

This option incorrectly applies the square of the binomial formula by omitting the cross-term generated by the product of 3a and 2b. The expression only reflects the squares of the first and second terms, disregarding the necessary middle term that arises from the binomial expansion.

This choice misrepresents the sign of the second term. While it correctly calculates the squares of both 3a and 2b, it erroneously adds them instead of subtracting the product of 3a and 2b multiplied by 2, which is necessary due to the binomial structure.

Here, the option fails to accurately compute the second square term (2b)², resulting in an incorrect negative term. The correct expansion should include a positive 4b² instead of the negative, as well as the correct coefficient for the middle term, leading to an overall incorrect expression.

This choice miscalculates the coefficient of the middle term. The correct expansion requires a coefficient of -12ab, derived from -2 times 3a times 2b, rather than the incorrect -6ab presented here.