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.