To solve the expression \((a - 3)(a + 5)\), you can use the distributive property (also known as the FOIL method for binomials):

\[
(a - 3)(a + 5) = a(a + 5) - 3(a + 5)
\]

Now, distribute each term:

\[
a \cdot a + a \cdot 5 - 3 \cdot a - 3 \cdot 5 = a^2 + 5a - 3a - 15
\]

Combine like terms:

\[
a^2 + 2a - 15
\]

So, \((a - 3)(a + 5)\) simplifies to:

\[
a^2 + 2a - 15
\]

Would you like any more details or have any questions about this solution? 

Here are 5 related questions to explore:
1. How would you factor the expression \(a^2 + 2a - 15\) back into binomials?
2. What is the value of the expression if \(a = 4\)?
3. How does the distributive property work with other polynomials?
4. Can you expand the expression \((a - 3)(a - 5)\)?
5. What are the roots of the equation \(a^2 + 2a - 15 = 0\)?

**Tip:** The FOIL method is a quick way to remember how to expand binomials: First, Outer, Inner, Last.

Learn how to solve the expression (a - 3)(a + 5) using the distributive property with a detailed step-by-step guide. This problem covers key algebraic concepts, including polynomials and the FOIL method. Suitable for students in Grades 7-9.

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