To simplify or expand $(x - 5)(x + 7)$, you can use the distributive property (also known as FOIL for binomials):

$(x - 5)(x + 7)$

1. Multiply the first terms: $x \cdot x = x^2$
2. Multiply the outer terms: $x \cdot 7 = 7x$
3. Multiply the inner terms: $-5 \cdot x = -5x$
4. Multiply the last terms: $-5 \cdot 7 = -35$

Now, combine these results:

$x^2 + 7x - 5x - 35$

Combine the like terms ($7x - 5x$):

$x^2 + 2x - 35$

Final Answer:

$x^2 + 2x - 35$

Would you like further explanation or have additional questions?

Here are some related questions to expand on this topic:

1. How do you factor quadratic expressions like $x^2 + 2x - 35$?
2. What are the roots of $x^2 + 2x - 35 = 0$?
3. Can this expression be graphed? What does the graph look like?
4. How would you verify the expansion of $(x - 5)(x + 7)$?
5. Can $(x - 5)(x + 7)$ be solved if it equals a specific value, like 0?

Tip: Remember that the FOIL method is a quick way to expand binomials systematically!