Work out the value of each expression when \( w=3, x=2, y=-4 \) and \( z=-2 \). \( \begin{array}{lll}\text { a } 3(w+x) & \text { b } x(2 w-y) & \text { c } \\ \text { d } w-z^{3} & \text { e } x^{2}+z^{2} & \text { f } \\ \text { d } w-y) \\ \text { g } \frac{x}{2}-\frac{y}{4} & \text { h } \frac{w x}{z}+y & (2 z)^{3} \\ \text { j } 20-2 w^{2} & \mathrm{k} & w+z(3 x-2 y)\end{array} \)

Sure! Let's evaluate each of the given expressions using the values \( w = 3 \), \( x = 2 \), \( y = -4 \), and \( z = -2 \). ### Given Values: - \( w = 3 \) - \( x = 2 \) - \( y = -4 \) - \( z = -2 \) ### Expressions and Their Evaluations: #### **a.** \( 3(w + x) \) \[ 3(w + x) = 3(3 + 2) = 3 \times 5 = \mathbf{15} \] #### **b.** \( x(2w - y) \) \[ x(2w - y) = 2(2 \times 3 - (-4)) = 2(6 + 4) = 2 \times 10 = \mathbf{20} \] #### **c.** *[No expression provided]* #### **d.** \( w - z^3 \) \[ w - z^3 = 3 - (-2)^3 = 3 - (-8) = 3 + 8 = \mathbf{11} \] #### **e.** \( x^2 + z^2 \) \[ x^2 + z^2 = 2^2 + (-2)^2 = 4 + 4 = \mathbf{8} \] #### **f.** \( w - y \) \[ w - y = 3 - (-4) = 3 + 4 = \mathbf{7} \] #### **g.** \( \frac{x}{2} - \frac{y}{4} \) \[ \frac{x}{2} - \frac{y}{4} = \frac{2}{2} - \frac{-4}{4} = 1 + 1 = \mathbf{2} \] #### **h.** \( \frac{w \times x}{z} + y \) \[ \frac{w \times x}{z} + y = \frac{3 \times 2}{-2} + (-4) = \frac{6}{-2} - 4 = -3 - 4 = \mathbf{-7} \] #### **i.** \( (2z)^3 \) \[ (2z)^3 = (2 \times -2)^3 = (-4)^3 = \mathbf{-64} \] #### **j.** \( 20 - 2w^2 \) \[ 20 - 2w^2 = 20 - 2 \times 3^2 = 20 - 2 \times 9 = 20 - 18 = \mathbf{2} \] #### **k.** \( w + z(3x - 2y) \) \[ w + z(3x - 2y) = 3 + (-2)(3 \times 2 - 2 \times (-4)) = 3 + (-2)(6 + 8) = 3 + (-2)(14) = 3 - 28 = \mathbf{-25} \] ### Summary of Evaluated Expressions: | **Expression** | **Value** | |---------------------------------|-----------| | a. \( 3(w + x) \) | **15** | | b. \( x(2w - y) \) | **20** | | c. *Not Provided* | | | d. \( w - z^3 \) | **11** | | e. \( x^2 + z^2 \) | **8** | | f. \( w - y \) | **7** | | g. \( \frac{x}{2} - \frac{y}{4} \) | **2** | | h. \( \frac{wx}{z} + y \) | **-7** | | i. \( (2z)^3 \) | **-64** | | j. \( 20 - 2w^2 \) | **2** | | k. \( w + z(3x - 2y) \) | **-25** | > **Note:** Expression **c** was not provided in your input. If you have any further questions or need additional assistance, feel free to ask!