Show all your working. 8 Work out the value of each expression when \( w=3, x=2, y=-4 \) and \( z=-2 \). \( \begin{array}{llll}\text { a } 3(w+x) & \text { b } x(2 w-y) & \text { c } & z(2 w-y) \\ \text { d } w-z^{3} & \text { e } x^{2}+z^{2} & \text { f } & (2 z)^{3} \\ \text { g } \frac{x}{2}-\frac{y}{4} & \text { h } \frac{w x}{z}+y & \text { i } & 2\left(x^{3}-z^{2}\right) \\ \text { j } 20-2 w^{2} & \text { k } w+z(3 x-2 y) & \text { l } & (3 z)^{2}-x^{5}\end{array} \)

Certainly! Let's evaluate each expression step by step using the given values: \[ w = 3, \quad x = 2, \quad y = -4, \quad z = -2 \] --- **a. \( 3(w + x) \)** 1. **Substitute the values:** \[ 3(3 + 2) \] 2. **Calculate inside the parentheses:** \[ 3(5) \] 3. **Multiply:** \[ 15 \] **Answer:** \( 15 \) --- **b. \( x(2w - y) \)** 1. **Substitute the values:** \[ 2(2 \times 3 - (-4)) \] 2. **Multiply \( 2 \times 3 \):** \[ 2(6 + 4) \] 3. **Simplify inside the parentheses:** \[ 2(10) \] 4. **Multiply:** \[ 20 \] **Answer:** \( 20 \) --- **c. \( z(2w - y) \)** 1. **Substitute the values:** \[ -2(2 \times 3 - (-4)) \] 2. **Multiply \( 2 \times 3 \):** \[ -2(6 + 4) \] 3. **Simplify inside the parentheses:** \[ -2(10) \] 4. **Multiply:** \[ -20 \] **Answer:** \( -20 \) --- **d. \( w - z^{3} \)** 1. **Substitute the values:** \[ 3 - (-2)^{3} \] 2. **Calculate \( (-2)^{3} \):** \[ 3 - (-8) \] 3. **Subtract (which becomes addition):** \[ 3 + 8 \] 4. **Add:** \[ 11 \] **Answer:** \( 11 \) --- **e. \( x^{2} + z^{2} \)** 1. **Substitute the values:** \[ 2^{2} + (-2)^{2} \] 2. **Calculate squares:** \[ 4 + 4 \] 3. **Add:** \[ 8 \] **Answer:** \( 8 \) --- **f. \( (2z)^{3} \)** 1. **Substitute the values:** \[ (2 \times -2)^{3} \] 2. **Multiply inside the parentheses:** \[ (-4)^{3} \] 3. **Calculate the cube:** \[ -64 \] **Answer:** \( -64 \) --- **g. \( \frac{x}{2} - \frac{y}{4} \)** 1. **Substitute the values:** \[ \frac{2}{2} - \frac{-4}{4} \] 2. **Simplify each fraction:** \[ 1 - (-1) \] 3. **Subtract (which becomes addition):** \[ 1 + 1 \] 4. **Add:** \[ 2 \] **Answer:** \( 2 \) --- **h. \( \frac{w x}{z} + y \)** 1. **Substitute the values:** \[ \frac{3 \times 2}{-2} + (-4) \] 2. **Multiply in the numerator:** \[ \frac{6}{-2} - 4 \] 3. **Divide:** \[ -3 - 4 \] 4. **Subtract:** \[ -7 \] **Answer:** \( -7 \) --- **i. \( 2\left(x^{3} - z^{2}\right) \)** 1. **Substitute the values:** \[ 2\left(2^{3} - (-2)^{2}\right) \] 2. **Calculate exponents:** \[ 2\left(8 - 4\right) \] 3. **Subtract inside the parentheses:** \[ 2(4) \] 4. **Multiply:** \[ 8 \] **Answer:** \( 8 \) --- **j. \( 20 - 2w^{2} \)** 1. **Substitute the values:** \[ 20 - 2 \times 3^{2} \] 2. **Calculate the square:** \[ 20 - 2 \times 9 \] 3. **Multiply:** \[ 20 - 18 \] 4. **Subtract:** \[ 2 \] **Answer:** \( 2 \) --- **k. \( w + z(3x - 2y) \)** 1. **Substitute the values:** \[ 3 + (-2)(3 \times 2 - 2 \times (-4)) \] 2. **Calculate inside the parentheses:** \[ 3 + (-2)(6 + 8) \] 3. **Simplify inside the parentheses:** \[ 3 + (-2)(14) \] 4. **Multiply:** \[ 3 - 28 \] 5. **Subtract:** \[ -25 \] **Answer:** \( -25 \) --- **l. \( (3z)^{2} - x^{5} \)** 1. **Substitute the values:** \[ (3 \times -2)^{2} - 2^{5} \] 2. **Multiply inside the parentheses:** \[ (-6)^{2} - 32 \] 3. **Calculate the square:** \[ 36 - 32 \] 4. **Subtract:** \[ 4 \] **Answer:** \( 4 \) --- ### **Summary of Results:** | Expression | Value | |------------|-------| | a. \( 3(w + x) \) | 15 | | b. \( x(2w - y) \) | 20 | | c. \( z(2w - y) \) | -20 | | d. \( w - z^{3} \) | 11 | | e. \( x^{2} + z^{2} \) | 8 | | f. \( (2z)^{3} \) | -64 | | g. \( \frac{x}{2} - \frac{y}{4} \) | 2 | | h. \( \frac{w x}{z} + y \) | -7 | | i. \( 2(x^{3} - z^{2}) \) | 8 | | j. \( 20 - 2w^{2} \) | 2 | | k. \( w + z(3x - 2y) \) | -25 | | l. \( (3z)^{2} - x^{5} \) | 4 |