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The problem shown in the image asks you to multiply two rational expressions and simplify the result. The expressions are:

\[
\frac{x^2 + 8x + 16}{x^2 - 11x} \times \frac{x^2 - 8x - 33}{x^2 + 7x + 12}
\]

### Step-by-step solution:

1. **Factor each expression**:

   - \(x^2 + 8x + 16\) factors as \((x + 4)(x + 4)\).
   - \(x^2 - 11x\) factors as \(x(x - 11)\).
   - \(x^2 - 8x - 33\) factors as \((x - 11)(x + 3)\).
   - \(x^2 + 7x + 12\) factors as \((x + 3)(x + 4)\).

2. **Rewrite the expression with the factored terms**:

   \[
   \frac{(x + 4)(x + 4)}{x(x - 11)} \times \frac{(x - 11)(x + 3)}{(x + 3)(x + 4)}
   \]

3. **Cancel out common factors**:

   - The \((x + 4)\) factor appears in both the numerator and denominator, so it can be canceled.
   - The \((x + 3)\) factor appears in both the numerator and denominator, so it can be canceled.
   - The \((x - 11)\) factor appears in both the numerator and denominator, so it can be canceled.

   After canceling, you're left with:

   \[
   \frac{x + 4}{x}
   \]

4. **Final simplified expression**:

   The final simplified result is:

   \[
   \frac{x + 4}{x}
   \]

Would you like further clarification on any step, or do you have any specific questions? Here are some related problems for practice:

1. How do you factor quadratic expressions?
2. What are common mistakes to avoid when multiplying rational expressions?
3. Can rational expressions ever be simplified into whole numbers?
4. What happens when the denominator of a rational expression is zero?
5. How does cross-canceling work in more complex fractions?

**Tip**: Always double-check factored forms to avoid missing any common terms that can be canceled.

Multiply and simplify: \(\frac{x^2 + 8x + 16}{x^2 - 11x} \times \frac{x^2 - 8x - 33}{x^2 + 7x + 12}\)

This tutorial covers how to multiply two rational expressions and simplify the result. It involves factoring quadratic expressions and canceling common terms. Key topics include factoring quadratics, multiplying rational expressions, and simplification techniques. Suitable for students in Grades 9-11.

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