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

Question

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

UpStudy AI · Accepted Answer

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 |
Here are the values of each expression when $$ w=3, x=2, y=-4, z=-2 $$: 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. $$ (3z)^{2} - x^{5} = 4 $$

Show all your working.
8 Work out the value of each expression when
and .

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Show all your working. 8 Work out the value of each expression when and .