To simplify the expression \((x - 7)(x + 2)\), we apply the distributive property (also known as FOIL: First, Outer, Inner, Last) to multiply the terms.

\[
(x - 7)(x + 2) = x(x + 2) - 7(x + 2)
\]

Now, distribute each term:

\[
= x^2 + 2x - 7x - 14
\]

Combine like terms:

\[
= x^2 - 5x - 14
\]

So, \((x - 7)(x + 2) = x^2 - 5x - 14\).

Would you like more details or have any questions? 

Here are 5 related questions you might find interesting:
1. How do you factor quadratic expressions like \(x^2 - 5x - 14\)?
2. What are the roots of the equation \(x^2 - 5x - 14 = 0\)?
3. Can this quadratic be solved by completing the square?
4. How does the distributive property work in polynomials?
5. What are the applications of expanding binomials?

**Tip**: When expanding binomials, always check for common terms you can combine to simplify your result.

Learn how to expand and simplify the binomial expression (x - 7)(x + 2) using the distributive property. This detailed step-by-step solution combines algebraic concepts, polynomial expansion, and factoring. Ideal for students in Grades 8-10.

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