a3−8ax2+x3;5a2x−6ax2−x3;3a3−5a2x−x3;a3+14ax2−x3


5a3−ax2−2x3−5a2x


5a3−5a2x


5a3−ax2−5a2x


5a3−2x3

It looks like you're working with polynomials involving two variables, \( a \) and \( x \). Let's analyze and simplify the polynomials you've provided. 

You provided the following expressions:
1. \( a^3 - 8a x^2 + x^3 \)
2. \( 5a^2 x - 6a x^2 - x^3 \)
3. \( 3a^3 - 5a^2 x - x^3 \)
4. \( a^3 + 14a x^2 - x^3 \)
5. \( 5a^3 - a x^2 - 2x^3 - 5a^2 x \)
6. \( 5a^3 - 5a^2 x \)
7. \( 5a^3 - a x^2 - 5a^2 x \)
8. \( 5a^3 - 2x^3 \)

### Summary of Terms in Each Expression:

- **1st expression**: Combines powers of \( a \) and \( x \), and contains the terms \( a^3 \), \( a x^2 \), and \( x^3 \).
- **2nd expression**: Includes terms with \( a^2 x \), \( a x^2 \), and \( x^3 \).
- **3rd expression**: Has terms with \( a^3 \), \( a^2 x \), and \( x^3 \).
- **4th expression**: Similar to the 1st, but with a different coefficient for \( a x^2 \).
- **5th expression**: More terms including \( a^3 \), \( a^2 x \), \( a x^2 \), and \( x^3 \).
- **6th, 7th, and 8th expressions**: These simplify further, focusing on \( a^3 \), \( a^2 x \), and \( x^3 \) terms.

### Next Steps:

Would you like me to:
1. Simplify each expression further?
2. Combine multiple expressions together?
3. Find common factors among the expressions?
4. Perform any specific operations on these polynomials (like adding or subtracting)?
5. Solve for \( a \) or \( x \) under certain conditions?

#### Tip:
When simplifying polynomials, grouping similar terms (like powers of \( a \) or \( x \)) can make further operations easier!

Let me know how you'd like to proceed!

a^3−8a x^2+x^3; 5a^2x−6a x^2−x^3; 3a^3−5a^2x−x^3; a^3+14a x^2−x^3; 5a^3−a x^2−2x^3−5a^2x; 5a^3−5a^2x; 5a^3−a x^2−5a^2x; 5a^3−2x^3

Explore how to simplify polynomial expressions involving multiple terms like a^3−8a x^2+x^3 and 5a^2x−6a x^2−x^3. This guide explains key algebraic concepts and provides a step-by-step solution for polynomial simplification. Ideal for students in Grades 9-12.

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