To simplify the given expression:

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

we need to combine like terms. Let's break it down step by step:

1. Group like terms:

• Combine the $x^3$ terms: $-4x^3 + 8x^3$
• Combine the $x^2$ terms: $-8x^2$ (there are no other $x^2$ terms)
• Combine the $x$ terms: $2x + x$
• Combine the constant terms: $-8 + 5$

2. Perform the addition:

• $x^3$: $-4x^3 + 8x^3 = 4x^3$
• $x^2$: $-8x^2$
• $x$: $2x + x = 3x$
• Constant: $-8 + 5 = -3$

3. Final expression:

The simplified expression is:

$4x^3 - 8x^2 + 3x - 3$

Would you like any further clarification on these steps?

Here are 5 related questions to further explore this topic:

1. What are the steps to combine like terms in an algebraic expression?
2. How do you arrange polynomials in standard form?
3. What is the importance of writing expressions in standard form?
4. How do you simplify expressions with higher degree terms like $x^3$?
5. What is the difference between a term with a variable and a constant term?

Tip: When simplifying expressions, always ensure to align terms with the same variable and degree before combining them.