8. \( 3(2 x-3)(x+2)-2(x-3)(x+3) \)

To simplify the expression \( 3(2x-3)(x+2) - 2(x-3)(x+3) \), you can start by expanding both components one at a time. First, for \( 3(2x-3)(x+2) \): 1. Expand \( (2x-3)(x+2) \) to get \( 2x^2 + 4x - 3x - 6 = 2x^2 + x - 6 \). 2. Then, multiply by 3: \( 3(2x^2 + x - 6) = 6x^2 + 3x - 18 \). Next, for \( -2(x-3)(x+3) \): 1. Recognize that \( (x-3)(x+3) \) is a difference of squares, which simplifies to \( x^2 - 9 \). 2. Thus, multiplying by -2 gives \( -2(x^2 - 9) = -2x^2 + 18 \). Now, combine both pieces together: \[ 6x^2 + 3x - 18 - 2x^2 + 18 = (6x^2 - 2x^2) + 3x + (-18 + 18) = 4x^2 + 3x. \] So, the simplified expression is \(\boxed{4x^2 + 3x}\).