1. Write an expression that is equivalent to \( (3 x-2)\left(x^{2}-2 x+4\right) \). Choose the correct answer in each drop down menu.

To find an expression equivalent to \( (3x - 2)(x^2 - 2x + 4) \), we can apply the distributive property (or FOIL method). First, we distribute \( 3x \) to each term in the second polynomial: \[ 3x \cdot x^2 = 3x^3, \] \[ 3x \cdot (-2x) = -6x^2, \] \[ 3x \cdot 4 = 12x. \] Now, distribute \( -2 \) to each term in the second polynomial: \[ -2 \cdot x^2 = -2x^2, \] \[ -2 \cdot (-2x) = 4x, \] \[ -2 \cdot 4 = -8. \] Now, we will combine all these results: \[ 3x^3 + (-6x^2 - 2x^2) + (12x + 4x) - 8. \] Combining like terms gives: \[ 3x^3 - 8x^2 + 16x - 8. \] Thus, an equivalent expression to \( (3x - 2)(x^2 - 2x + 4) \) is: \( 3x^3 - 8x^2 + 16x - 8. \)