simplifying polynomials Math Worksheets, Math Practice for Kids. - Free Printable

Let's solve each polynomial expression step by step. We will simplify each expression by combining like terms and distributing where necessary.

---

1. $ 6x^2 - 9x^2 - 6x^2 - 5x^2 - 8x^2 $

Combine all the $ x^2 $ terms:

$$
(6 - 9 - 6 - 5 - 8)x^2 = (-22)x^2 = \boxed{-22x^2}
$$

---

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

First, combine like terms: $ x + 8x - x = 8x $

Now distribute the $-4$:

$$
-4(7x^3 - 4x) = -28x^3 + 16x
$$

Now add everything:

$$
8x + (-28x^3 + 16x) = -28x^3 + (8x + 16x) = \boxed{-28x^3 + 24x}
$$

---

3. $ 9x^2 + 5x - 2(2x^3 - 6x) - 8x^2 $

Distribute the $-2$:

$$
-2(2x^3 - 6x) = -4x^3 + 12x
$$

Now combine all terms:

$$
9x^2 + 5x - 4x^3 + 12x - 8x^2
$$

Group like terms:

- $ -4x^3 $
- $ (9x^2 - 8x^2) = x^2 $
- $ (5x + 12x) = 17x $

Result: $ \boxed{-4x^3 + x^2 + 17x} $

---

4. $ 5x^2 + x^3 - 2(5x - 2x^2) + 2x $

Distribute the $-2$:

$$
-2(5x - 2x^2) = -10x + 4x^2
$$

Now combine all:

$$
x^3 + 5x^2 + 4x^2 - 10x + 2x = x^3 + (5x^2 + 4x^2) + (-10x + 2x)
$$

$$
= \boxed{x^3 + 9x^2 - 8x}
$$

---

5. $ x + 7x + 2(6x^2 + 9x) + 7x $

Combine $ x + 7x + 7x = 15x $

Distribute the 2:

$$
2(6x^2 + 9x) = 12x^2 + 18x
$$

Now add:

$$
15x + 12x^2 + 18x = 12x^2 + (15x + 18x) = \boxed{12x^2 + 33x}
$$

---

6. $ 3x^3 + 4x^3 + 6x + 3(2x - 9x^2) $

Combine like terms: $ 3x^3 + 4x^3 = 7x^3 $

Distribute the 3:

$$
3(2x - 9x^2) = 6x - 27x^2
$$

Now combine:

$$
7x^3 + 6x - 27x^2 + 6x = 7x^3 - 27x^2 + (6x + 6x) = \boxed{7x^3 - 27x^2 + 12x}
$$

---

7. $ 8x + 9x^3 + 3x^3 - 7x^2 + 5x^2 $

Group like terms:

- $ 9x^3 + 3x^3 = 12x^3 $
- $ -7x^2 + 5x^2 = -2x^2 $
- $ 8x $ remains

So: $ \boxed{12x^3 - 2x^2 + 8x} $

---

8. $ 8x - 2x - 3x^3 - 4(4x^3 - 3x^2) $

Simplify $ 8x - 2x = 6x $

Distribute $-4$:

$$
-4(4x^3 - 3x^2) = -16x^3 + 12x^2
$$

Now combine:

$$
6x - 3x^3 - 16x^3 + 12x^2 = -19x^3 + 12x^2 + 6x
$$

Result: $ \boxed{-19x^3 + 12x^2 + 6x} $

---

9. $ 5x^3 + 8x^3 - 4(2x^2 - 5x^3) + 6x $

Combine $ 5x^3 + 8x^3 = 13x^3 $

Distribute $-4$:

$$
-4(2x^2 - 5x^3) = -8x^2 + 20x^3
$$

Now combine:

$$
13x^3 + 20x^3 = 33x^3 \\
-8x^2 \\
+6x
$$

So: $ \boxed{33x^3 - 8x^2 + 6x} $

---

10. $ 5x + 6x^3 - x^3 + 9x^3 - 4x^3 $

Combine $ x^3 $ terms:

$$
6x^3 - x^3 + 9x^3 - 4x^3 = (6 - 1 + 9 - 4)x^3 = 10x^3
$$

Then $ +5x $

Result: $ \boxed{10x^3 + 5x} $

---

✔ Final Answers:

1. $ -22x^2 $
2. $ -28x^3 + 24x $
3. $ -4x^3 + x^2 + 17x $
4. $ x^3 + 9x^2 - 8x $
5. $ 12x^2 + 33x $
6. $ 7x^3 - 27x^2 + 12x $
7. $ 12x^3 - 2x^2 + 8x $
8. $ -19x^3 + 12x^2 + 6x $
9. $ 33x^3 - 8x^2 + 6x $
10. $ 10x^3 + 5x $

---

Let me know if you'd like these formatted for printing or want a check of any specific problem!