\( \left. \begin{array} { l } { ( 2 x - 3 ) ( 3 x + 2 ) = } \\ { ( 2 x - 3 ) ( 2 x + 1 ) = } \\ { ( 3 x - 2 ) ( 2 x + 3 ) = } \\ { ( 3 x - 2 ) ( 2 x - 3 ) = } \end{array} \right. \)

**1. Expanding \((2x-3)(3x+2)\):** - Multiply the first terms: \(\quad 2x \cdot 3x = 6x^2\) - Multiply the outer terms: \(\quad 2x \cdot 2 = 4x\) - Multiply the inner terms: \(\quad (-3) \cdot 3x = -9x\) - Multiply the last terms: \(\quad (-3) \cdot 2 = -6\) - Combine like terms: \[ 6x^2 + 4x - 9x - 6 = 6x^2 - 5x - 6 \] --- **2. Expanding \((2x-3)(2x+1)\):** - Multiply the first terms: \(\quad 2x \cdot 2x = 4x^2\) - Multiply the outer terms: \(\quad 2x \cdot 1 = 2x\) - Multiply the inner terms: \(\quad (-3) \cdot 2x = -6x\) - Multiply the last terms: \(\quad (-3) \cdot 1 = -3\) - Combine like terms: \[ 4x^2 + 2x - 6x - 3 = 4x^2 - 4x - 3 \] --- **3. Expanding \((3x-2)(2x+3)\):** - Multiply the first terms: \(\quad 3x \cdot 2x = 6x^2\) - Multiply the outer terms: \(\quad 3x \cdot 3 = 9x\) - Multiply the inner terms: \(\quad (-2) \cdot 2x = -4x\) - Multiply the last terms: \(\quad (-2) \cdot 3 = -6\) - Combine like terms: \[ 6x^2 + 9x - 4x - 6 = 6x^2 + 5x - 6 \] --- **4. Expanding \((3x-2)(2x-3)\):** - Multiply the first terms: \(\quad 3x \cdot 2x = 6x^2\) - Multiply the outer terms: \(\quad 3x \cdot (-3) = -9x\) - Multiply the inner terms: \(\quad (-2) \cdot 2x = -4x\) - Multiply the last terms: \(\quad (-2) \cdot (-3) = 6\) - Combine like terms: \[ 6x^2 - 9x - 4x + 6 = 6x^2 - 13x + 6 \]