(x−7)(x$$ \placeholder{}^2 $$-x-3)$$  $$

It seems there was a placeholder or some formatting issue in your equation. Based on what you've written, it looks like you're trying to multiply two expressions together, but there's some missing information. 

Let me try to reconstruct it:

The expression you might be looking at could be:

\[
(x - 7)(x^2 - x - 3)
\]

Would you like to expand this expression? If so, you would distribute the $(x - 7)$ across the terms in $(x^2 - x - 3)$.

If this assumption is correct, the expansion would proceed as follows:

\[
(x - 7)(x^2 - x - 3) = x(x^2 - x - 3) - 7(x^2 - x - 3)
\]

Expanding each part:

\[
= x^3 - x^2 - 3x - 7x^2 + 7x + 21
\]

Now, combine like terms:

\[
= x^3 - 8x^2 + 4x + 21
\]

So, the expanded expression is:

\[
x^3 - 8x^2 + 4x + 21
\]

If this wasn't what you intended, feel free to clarify or provide more details! 

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Would you like more details or have any questions? Here are some related questions:

1. How do you factor cubic polynomials?
2. What are the steps for expanding binomials and trinomials?
3. How do you find the roots of the polynomial $x^3 - 8x^2 + 4x + 21$?
4. Can you graph the function $x^3 - 8x^2 + 4x + 21$?
5. What is the significance of the discriminant in quadratic expressions?

**Tip:** When expanding expressions, always distribute carefully and then combine like terms to simplify the result.

Learn how to expand the expression (x - 7)(x^2 - x - 3) with a detailed step-by-step solution. This problem covers key algebraic concepts, including polynomials and the distributive property. Suitable for students in Grades 9-12.

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