(5) $$ (9-2)^{2}-\left|2^{2}-3^{2}\right|+2 $$ (6) $$ \frac{8\left[14-\left(7+4^{2}\right)\right]}{|-12|-|-8|} $$ 4m²-5m when $$ m=-4 $$ (8) $$ 3 x^{2} y-y^{2} $$ when $$ x=-2 $$ and $$ y=5 $$

Question

UpStudy AI · Accepted Answer

Sure! Let's solve each of the given expressions step-by-step.

---

### **Problem (5)**

$$
(9-2)^{2} - \left|2^{2} - 3^{2}\right| + 2
$$

**Steps:**

1. **Calculate inside the first parentheses:**
   $$
   9 - 2 = 7
   $$
   
2. **Square the result:**
   $$
   7^{2} = 49
   $$
   
3. **Calculate inside the absolute value:**
   $$
   2^{2} - 3^{2} = 4 - 9 = -5
   $$
   
4. **Apply the absolute value:**
   $$
   |-5| = 5
   $$
   
5. **Substitute back into the expression:**
   $$
   49 - 5 + 2 = 46
   $$
   
**Answer:**  
$$
46
$$

---

### **Problem (6)**

$$
\frac{8\left[14 - \left(7 + 4^{2}\right)\right]}{\,|-12| - |-8|\,}
$$

**Steps:**

1. **Calculate inside the innermost parentheses:**
   $$
   4^{2} = 16
   $$
   $$
   7 + 16 = 23
   $$
   
2. **Subtract from 14:**
   $$
   14 - 23 = -9
   $$
   
3. **Multiply by 8:**
   $$
   8 \times (-9) = -72
   $$
   
4. **Calculate the absolute values in the denominator:**
   $$
   |-12| = 12 \quad \text{and} \quad |-8| = 8
   $$
   
5. **Subtract the absolute values:**
   $$
   12 - 8 = 4
   $$
   
6. **Divide the numerator by the denominator:**
   $$
   \frac{-72}{4} = -18
   $$
   
**Answer:**  
$$
-18
$$

---

### **Problem (7)**

Evaluate $$4m^{2} - 5m$$ when $$m = -4$$.

**Steps:**

1. **Substitute $$m = -4$$ into the expression:**
   $$
   4(-4)^{2} - 5(-4)
   $$
   
2. **Calculate the square:**
   $$
   (-4)^{2} = 16
   $$
   
3. **Multiply by 4:**
   $$
   4 \times 16 = 64
   $$
   
4. **Multiply -5 by -4:**
   $$
   -5 \times (-4) = 20
   $$
   
5. **Add the results:**
   $$
   64 + 20 = 84
   $$
   
**Answer:**  
$$
84
$$

---

### **Problem (8)**

Evaluate $$3x^{2}y - y^{2}$$ when $$x = -2$$ and $$y = 5$$.

**Steps:**

1. **Substitute $$x = -2$$ and $$y = 5$$ into the expression:**
   $$
   3(-2)^{2}(5) - 5^{2}
   $$
   
2. **Calculate the square of $$x$$:**
   $$
   (-2)^{2} = 4
   $$
   
3. **Multiply by 3 and then by $$y$$:**
   $$
   3 \times 4 \times 5 = 60
   $$
   
4. **Calculate the square of $$y$$:**
   $$
   5^{2} = 25
   $$
   
5. **Subtract the squared term from the first part:**
   $$
   60 - 25 = 35
   $$
   
**Answer:**  
$$
35
$$

---

If you have any further questions or need additional explanations, feel free to ask!
**Problem (5):** $$ (9-2)^{2} - \left|2^{2} - 3^{2}\right| + 2 = 46 $$ **Problem (6):** $$ \frac{8\left[14 - \left(7 + 4^{2}\right)\right]}{\,|-12| - |-8|\,} = -18 $$ **Problem (7):** When $$m = -4$$, $$ 4m^{2} - 5m = 84 $$ **Problem (8):** When $$x = -2$$ and $$y = 5$$, $$ 3x^{2}y - y^{2} = 35 $$

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