28. $$ (6 x+9)-(7 x+1) $$ 30. $$ \left(4 m^{2}-m+2\right)-\left(-3 m^{2}+10 m+4\right) $$ 32. $$ (-r-10)-\left(-4 r^{3}+r^{2}+7 r\right) $$ 34. $$ \left(4.5 d-6 d^{3}+3 d^{2}\right)-\left(10 d^{3}+7 d^{2}-25\right) $$

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UpStudy AI · Accepted Answer

Sure! Let's simplify each of the given algebraic expressions step by step.

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### **Problem 28**
$$
(6x + 9) - (7x + 1)
$$

**Step 1:** Distribute the negative sign to the second parenthesis.
$$
6x + 9 - 7x - 1
$$

**Step 2:** Combine like terms.
$$
(6x - 7x) + (9 - 1) = -x + 8
$$

**Answer:**
$$
-\,x + 8
$$

---

### **Problem 30**
$$
\left(4m^{2} - m + 2\right) - \left(-3m^{2} + 10m + 4\right)
$$

**Step 1:** Distribute the negative sign to the second parenthesis.
$$
4m^{2} - m + 2 + 3m^{2} - 10m - 4
$$

**Step 2:** Combine like terms.
$$
(4m^{2} + 3m^{2}) + (-m - 10m) + (2 - 4) = 7m^{2} - 11m - 2
$$

**Answer:**
$$
7m^{2} - 11m - 2
$$

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### **Problem 32**
$$
(-r - 10) - \left(-4r^{3} + r^{2} + 7r\right)
$$

**Step 1:** Distribute the negative sign to the second parenthesis.
$$
- r - 10 + 4r^{3} - r^{2} - 7r
$$

**Step 2:** Rearrange and combine like terms.
$$
4r^{3} - r^{2} + (-r - 7r) - 10 = 4r^{3} - r^{2} - 8r - 10
$$

**Answer:**
$$
4r^{3} - r^{2} - 8r - 10
$$

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### **Problem 34**
$$
\left(4.5d - 6d^{3} + 3d^{2}\right) - \left(10d^{3} + 7d^{2} - 25\right)
$$

**Step 1:** Distribute the negative sign to the second parenthesis.
$$
4.5d - 6d^{3} + 3d^{2} - 10d^{3} - 7d^{2} + 25
$$

**Step 2:** Combine like terms.
$$
(-6d^{3} - 10d^{3}) + (3d^{2} - 7d^{2}) + 4.5d + 25 = -16d^{3} - 4d^{2} + 4.5d + 25
$$

**Answer:**
$$
-16d^{3} - 4d^{2} + 4.5d + 25
$$

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Feel free to reach out if you have any more questions!
Here are the simplified answers for each problem: 1. **Problem 28:** $$ -x + 8 $$ 2. **Problem 30:** $$ 7m^{2} - 11m - 2 $$ 3. **Problem 32:** $$ 4r^{3} - r^{2} - 8r - 10 $$ 4. **Problem 34:** $$ -16d^{3} - 4d^{2} + 4.5d + 25 $$ If you have any more questions, feel free to ask!

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