1. The problem is to expand the expression $ (3x - 2y)^2 $. 2. We use the formula for the square of a binomial: $$ (a - b)^2 = a^2 - 2ab + b^2 $$ where $a = 3x$ and $b = 2y$. 3. Substitute $a$ and $b$ into the formula: $$ (3x - 2y)^2 = (3x)^2 - 2 \times 3x \times 2y + (2y)^2 $$ 4. Calculate each term: - $(3x)^2 = 9x^2$ - $-2 \times 3x \times 2y = -12xy$ - $(2y)^2 = 4y^2$ 5. Combine all terms: $$ 9x^2 - 12xy + 4y^2 $$ 6. Therefore, the expanded form of $ (3x - 2y)^2 $ is $9x^2 - 12xy + 4y^2$.