Answer
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. \( (3z)^{2} - x^{5} = 4 \)
Solution
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 |
Reviewed and approved by the UpStudy tutoring team
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