2) \( \quad-2 x(3 x-4)^{2}+5(x+2)(2 x-3)-4(2 x-3 \)

To simplify the expression \( -2x(3x-4)^{2} + 5(x+2)(2x-3) - 4(2x-3) \), let's break it down step by step. First, let's expand each term in the expression: 1. For the first term \( -2x(3x-4)^{2} \): - Start with \( (3x-4)^{2} = 9x^{2} - 24x + 16 \). - Then, multiply by \( -2x \): \[ -2x(9x^{2} - 24x + 16) = -18x^{3} + 48x^{2} - 32x \] 2. For the second term \( 5(x+2)(2x-3) \): - Expand \( (x+2)(2x-3) = 2x^{2} - 3x + 4x - 6 = 2x^{2} + x - 6 \). - Then, multiply by \( 5 \): \[ 5(2x^{2} + x - 6) = 10x^{2} + 5x - 30 \] 3. For the third term \( -4(2x-3) \): - Distributing gives: \[ -4(2x-3) = -8x + 12 \] Now, we can combine all expanded terms: \[ -18x^{3} + 48x^{2} - 32x + 10x^{2} + 5x - 30 - 8x + 12 \] Combine like terms: - The cubic term: \( -18x^{3} \) - The quadratic terms: \( 48x^{2} + 10x^{2} = 58x^{2} \) - The linear terms: \( -32x + 5x - 8x = -35x \) - The constant terms: \( -30 + 12 = -18 \) Putting it all together, we have: \[ -18x^{3} + 58x^{2} - 35x - 18 \] So, the simplified expression is: \[ \boxed{-18x^{3} + 58x^{2} - 35x - 18} \]