The given expression is:

\[
(x^3 - 3x^2 - 2x^2 + 6x)(x^2 - 7x - 4x + 28)
\]

Let’s first simplify both parts of the expression before expanding.

### Step 1: Simplify each part

For the first part:
\[
x^3 - 3x^2 - 2x^2 + 6x = x^3 - 5x^2 + 6x
\]

For the second part:
\[
x^2 - 7x - 4x + 28 = x^2 - 11x + 28
\]

### Step 2: Multiply the two expressions
We now have:
\[
(x^3 - 5x^2 + 6x)(x^2 - 11x + 28)
\]
We expand this by multiplying each term in the first expression by each term in the second expression.

\[
x^3(x^2 - 11x + 28) = x^5 - 11x^4 + 28x^3
\]
\[
-5x^2(x^2 - 11x + 28) = -5x^4 + 55x^3 - 140x^2
\]
\[
6x(x^2 - 11x + 28) = 6x^3 - 66x^2 + 168x
\]

### Step 3: Combine like terms

Now, we combine all the terms from the expansion:

\[
x^5 - 11x^4 + 28x^3 - 5x^4 + 55x^3 - 140x^2 + 6x^3 - 66x^2 + 168x
\]

Simplifying further:
\[
x^5 + (-11x^4 - 5x^4) + (28x^3 + 55x^3 + 6x^3) + (-140x^2 - 66x^2) + 168x
\]
\[
x^5 - 16x^4 + 89x^3 - 206x^2 + 168x
\]

### Final Answer:
The simplified expression is:
\[
x^5 - 16x^4 + 89x^3 - 206x^2 + 168x
\]

Would you like more details on any of the steps, or do you have further questions?

Here are some related questions:
1. How do you multiply two polynomials in general?
2. What is the degree of the resulting polynomial after multiplication?
3. How do you apply the distributive property in polynomial multiplication?
4. How can polynomial division work with higher-degree polynomials?
5. What is the difference between simplifying and expanding expressions?

**Tip:** Always simplify individual polynomial expressions before multiplying them for easier calculations!

This tutorial shows how to simplify and expand the polynomial expression (x³-3x²+6x)(x²-7x+28) using polynomial multiplication and algebraic expansion. Learn step-by-step methods to handle polynomial simplification and combining like terms. Ideal for students in Grades 9-12.

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