(s+r) (×) (×³+2×²-4×-8)+(×²+×-2)

Let's simplify and expand the given expression:

\[
(s + r) \times (x^3 + 2x^2 - 4x - 8) + (x^2 + x - 2)
\]

### Step 1: Expand \((s + r) \times (x^3 + 2x^2 - 4x - 8)\)

Each term in \(s + r\) multiplies with every term in \(x^3 + 2x^2 - 4x - 8\):

\[
= s \times (x^3 + 2x^2 - 4x - 8) + r \times (x^3 + 2x^2 - 4x - 8)
\]

This can be expanded as:

\[
= s \times x^3 + s \times 2x^2 - s \times 4x - s \times 8 + r \times x^3 + r \times 2x^2 - r \times 4x - r \times 8
\]

Combining like terms:

\[
= (s + r)x^3 + (s + r)2x^2 - (s + r)4x - (s + r)8
\]

\[
= (s + r)(x^3 + 2x^2 - 4x - 8)
\]

### Step 2: Add the expression \(x^2 + x - 2\)

So, we have:

\[
(s + r)(x^3 + 2x^2 - 4x - 8) + (x^2 + x - 2)
\]

### Final Expression:

The final expression is:

\[
(s + r)(x^3 + 2x^2 - 4x - 8) + (x^2 + x - 2)
\]

This represents a polynomial expression that is influenced by the sum \(s + r\). 

Would you like to explore further or simplify this expression in any particular direction?

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**Relative Questions:**

1. How do you expand and simplify polynomials?
2. What are the steps to combine like terms in algebraic expressions?
3. How does distributing work in algebra?
4. Can you explain polynomial addition and subtraction?
5. How do you factor complex polynomials?

**Tip**: Always expand and combine like terms in an expression systematically to avoid errors and simplify the process.

Learn how to simplify and expand the polynomial expression (s + r)(x^3 + 2x^2 - 4x - 8) + (x^2 + x - 2). This problem involves polynomial operations, including expansion and addition of algebraic terms. Suitable for high school students and beyond.

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