https://file.aiquickdraw.com/mathbot/file/1727918677069tezk55wa.jpg

I see that you've uploaded a list of expressions to simplify. I'll go through each expression step by step and provide the simplified result.

### 1) \((5p^2 - 3) + (2p^2 - 3p^3)\)
Simplifying:
\[
(5p^2 + 2p^2) - 3 - 3p^3 = 7p^2 - 3p^3 - 3
\]

### 2) \((a^3 - 2a^2) - (3a^2 - 4a^3)\)
Simplifying:
\[
a^3 - 2a^2 - 3a^2 + 4a^3 = (a^3 + 4a^3) - (2a^2 + 3a^2) = 5a^3 - 5a^2
\]

### 3) \((4 + 2n^3) + (5n^3 + 2)\)
Simplifying:
\[
(4 + 2) + (2n^3 + 5n^3) = 6 + 7n^3
\]

### 4) \((4n - 3n^3) - (3n^3 + 4n)\)
Simplifying:
\[
4n - 3n^3 - 3n^3 - 4n = (-3n^3 - 3n^3) + (4n - 4n) = -6n^3
\]

### 5) \((3a^2 + 1) - (4 + 2a^2)\)
Simplifying:
\[
(3a^2 - 2a^2) + (1 - 4) = a^2 - 3
\]

### 6) \((4r^3 + 3r^4) - (r^4 - 5r^3)\)
Simplifying:
\[
(4r^3 + 5r^3) + (3r^4 - r^4) = 9r^3 + 2r^4
\]

### 7) \((5a + 4) - (5a + 3)\)
Simplifying:
\[
(5a - 5a) + (4 - 3) = 1
\]

### 8) \((3x^4 - 3x) - (3x - 3x^4)\)
Simplifying:
\[
(3x^4 + 3x^4) - (3x - 3x) = 6x^4
\]

### 9) \((-4k^4 + 14 + 3k^2) + (-3k^4 - 14k^2 - 8)\)
Simplifying:
\[
(-4k^4 - 3k^4) + (3k^2 - 14k^2) + (14 - 8) = -7k^4 - 11k^2 + 6
\]

### 10) \((3 - 6n^5 - 8n^4) - (-6n^4 - 3n - 8n^5)\)
Simplifying:
\[
3 - 6n^5 - 8n^4 + 6n^4 + 3n + 8n^5 = 3 + 3n + (8n^5 - 6n^5) + (-8n^4 + 6n^4) = 3 + 3n + 2n^5 - 2n^4
\]

### 11) \((12a^5 - 6a - 10a^3) - (10a^5 - 2a^5 - 14a^4)\)
Simplifying:
\[
(12a^5 - 10a^5) - (-2a^5) + (-6a - 0) - (10a^3) = 2a^5 - 10a^3 - 6a
\]

### 12) \((8n - 3n^4 + 10n^2) - (3n^2 + 11n^4 - 7)\)
Simplifying:
\[
(8n - 0) + (10n^2 - 3n^2) + (-3n^4 + 11n^4) + 7 = 8n + 7n^2 + 8n^4 - 7
\]

### 13) \((-x^4 + 13x^5 + 6x^3) + (6x^3 + 5x^5 + 7x^4)\)
Simplifying:
\[
(-x^4 + 7x^4) + (13x^5 + 5x^5) + (6x^3 + 6x^3) = 6x^4 + 18x^5 + 12x^3
\]

### 14) \((9r^3 + 5r^2 + 11r) + (-2r^3 + 9r - 8r^2)\)
Simplifying:
\[
(9r^3 - 2r^3) + (5r^2 - 8r^2) + (11r + 9r) = 7r^3 - 3r^2 + 20r
\]

---

Would you like any further details or explanations on these steps?

Here are 5 related questions you might explore:
1. How do you combine like terms in polynomial expressions?
2. What are the key differences between addition and subtraction of polynomials?
3. How do exponents affect the simplification of terms in polynomial expressions?
4. What role do negative signs play in distributing terms across parentheses?
5. How can you factor a polynomial after simplifying it?

**Tip:** Always organize like terms by degree to simplify polynomial expressions efficiently.

Learn how to simplify the polynomial expression (5p² - 3) + (2p² - 3p³) by combining like terms. This problem covers core algebraic concepts such as combining like terms and polynomial simplification. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation