Simplifying Polynomials worksheet with 12 algebraic expressions for practice.

Let's solve each polynomial simplification problem step by step. The goal is to combine like terms — terms that have the same variable raised to the same power.

---

1. $ 10x^3 - 2x^2 + 5x^3 - 6x^2 $

Group like terms:
- $10x^3 + 5x^3 = 15x^3$
- $-2x^2 - 6x^2 = -8x^2$

✔ Answer: $15x^3 - 8x^2$

---

2. $5r^5 - 2r^2 + 5r^5 - 6r^2$

Group like terms:
- $5r^5 + 5r^5 = 10r^5$
- $-2r^2 - 6r^2 = -8r^2$

✔ Answer: $10r^5 - 8r^2$

---

3. $2x^3 - 7x^2 + 2x^3 - 6x^2$

Group like terms:
- $2x^3 + 2x^3 = 4x^3$
- $-7x^2 - 6x^2 = -13x^2$

✔ Answer: $4x^3 - 13x^2$

---

4. $10n^4 - 3n^2 + 9n^3 - 5n^2$

Group like terms:
- $10n^4$ (only one term)
- $9n^3$ (only one term)
- $-3n^2 - 5n^2 = -8n^2$

✔ Answer: $10n^4 + 9n^3 - 8n^2$

---

5. $10x^2 + 4x^4 + 6x^3 - 3x^2$

Group like terms:
- $4x^4$ (only one)
- $6x^3$ (only one)
- $10x^2 - 3x^2 = 7x^2$

Arrange in descending order of exponents:

✔ Answer: $4x^4 + 6x^3 + 7x^2$

---

6. $3x^3 + 2x^2 + 5x^3 - 2x^5$

Group like terms:
- $-2x^5$ (only one)
- $3x^3 + 5x^3 = 8x^3$
- $2x^2$ (only one)

Arrange in descending order:

✔ Answer: $-2x^5 + 8x^3 + 2x^2$

---

7. $3(9x^3 - 4x^2 + x^3 - 2x^2)$

First, simplify inside the parentheses:
- $9x^3 + x^3 = 10x^3$
- $-4x^2 - 2x^2 = -6x^2$

So: $3(10x^3 - 6x^2)$

Now distribute the 3:
- $3 \cdot 10x^3 = 30x^3$
- $3 \cdot (-6x^2) = -18x^2$

✔ Answer: $30x^3 - 18x^2$

---

8. $4(2x^3 - 6x^2) + 2x^3 - 7x^2$

Distribute the 4:
- $4 \cdot 2x^3 = 8x^3$
- $4 \cdot (-6x^2) = -24x^2$

Now add the rest:
- $8x^3 + 2x^3 = 10x^3$
- $-24x^2 - 7x^2 = -31x^2$

✔ Answer: $10x^3 - 31x^2$

---

9. $10t^3 - 6t^2 + 3t^3 - 9t^2$

Group like terms:
- $10t^3 + 3t^3 = 13t^3$
- $-6t^2 - 9t^2 = -15t^2$

✔ Answer: $13t^3 - 15t^2$

---

10. $x^5 - 5x^2 + 5x^3 - 8x^2$

Group like terms:
- $x^5$ (only one)
- $5x^3$ (only one)
- $-5x^2 - 8x^2 = -13x^2$

Arrange in descending order:

✔ Answer: $x^5 + 5x^3 - 13x^2$

---

11. $7x^2 - 6x^3 + 5x^3 - 4x^2$

Group like terms:
- $-6x^3 + 5x^3 = -x^3$
- $7x^2 - 4x^2 = 3x^2$

✔ Answer: $-x^3 + 3x^2$

---

12. $11x^3 + 6x^2 + 3x^3 - x^2$

Group like terms:
- $11x^3 + 3x^3 = 14x^3$
- $6x^2 - x^2 = 5x^2$

✔ Answer: $14x^3 + 5x^2$

---

✔ Final Answers:

1. $15x^3 - 8x^2$
2. $10r^5 - 8r^2$
3. $4x^3 - 13x^2$
4. $10n^4 + 9n^3 - 8n^2$
5. $4x^4 + 6x^3 + 7x^2$
6. $-2x^5 + 8x^3 + 2x^2$
7. $30x^3 - 18x^2$
8. $10x^3 - 31x^2$
9. $13t^3 - 15t^2$
10. $x^5 + 5x^3 - 13x^2$
11. $-x^3 + 3x^2$
12. $14x^3 + 5x^2$

---

Let me know if you'd like these written neatly or formatted for printing!