The given expression is:

\[
(x - 5)\sqrt{x + 7}
\]

This expression cannot be simplified further algebraically without additional information. However, here are some points to consider:

1. **Domain**: The expression involves a square root function, and square roots are only defined for non-negative values. Therefore, for the expression to be valid, \(x + 7 \geq 0\), which implies \(x \geq -7\).

2. **Critical Points**: To analyze the behavior of this expression further (such as finding maxima, minima, or other important points), you might want to take the derivative or solve for specific values.

Would you like to evaluate it at a specific point or analyze its behavior further?

Here are 5 related questions:
1. What is the domain of the expression \( (x-5)\sqrt{x+7} \)?
2. How do you find the derivative of \( (x-5)\sqrt{x+7} \)?
3. How does the expression behave as \(x\) approaches its boundaries, like \(x = -7\)?
4. What are the critical points of the function \( (x-5)\sqrt{x+7} \)?
5. How can this expression be used in an applied problem, such as finding a maximum or minimum value?

**Tip**: Always check the domain of a function with square roots to avoid dealing with undefined expressions!

Explore the algebraic expression (x-5)√(x+7), focusing on its domain, critical points, and behavior near boundaries. This expression is particularly useful for understanding square root functions and domain restrictions, suitable for high school students (Grades 9-12).

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