To solve the expression \( (x^2 + x - 2) \cdot (x - 4) \), we need to distribute each term in the first polynomial \( (x^2 + x - 2) \) by each term in the second polynomial \( (x - 4) \).

Here's the step-by-step process:

\[
(x^2 + x - 2) \cdot (x - 4)
\]

### Step 1: Distribute each term in \( (x^2 + x - 2) \) by \( x \):

- \( x^2 \cdot x = x^3 \)
- \( x \cdot x = x^2 \)
- \( -2 \cdot x = -2x \)

This gives:

\[
x^3 + x^2 - 2x
\]

### Step 2: Distribute each term in \( (x^2 + x - 2) \) by \( -4 \):

- \( x^2 \cdot (-4) = -4x^2 \)
- \( x \cdot (-4) = -4x \)
- \( -2 \cdot (-4) = 8 \)

This gives:

\[
-4x^2 - 4x + 8
\]

### Step 3: Add both results:

Now, combine the like terms from both steps:

\[
x^3 + x^2 - 2x - 4x^2 - 4x + 8
\]

Combine like terms:

- \( x^2 - 4x^2 = -3x^2 \)
- \( -2x - 4x = -6x \)

So the final expression is:

\[
x^3 - 3x^2 - 6x + 8
\]

This is the expanded form of \( (x^2 + x - 2) \cdot (x - 4) \).

Would you like further clarification or additional details?

### Related questions:
1. How do you multiply polynomials with more than two terms?
2. What is the importance of combining like terms in polynomial multiplication?
3. How can factoring help in solving polynomial equations?
4. How do you find the roots of a cubic polynomial like \( x^3 - 3x^2 - 6x + 8 \)?
5. What are the common methods for simplifying polynomial expressions?

### Tip:
When multiplying polynomials, always be careful to distribute every term to avoid missing terms or making errors.

Explore the solution for multiplying two polynomials: (x² + x - 2) × (x - 4). This problem covers polynomial expansion using the distributive property and combining like terms. Suitable for students in Grades 8-10.

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