To simplify the expression \((x - 1)(x + 3)\), we can use the distributive property (also known as the FOIL method for binomials). Here's how it's done step by step:

\[
(x - 1)(x + 3)
\]

1. Multiply the first terms: \(x \times x = x^2\)
2. Multiply the outer terms: \(x \times 3 = 3x\)
3. Multiply the inner terms: \(-1 \times x = -x\)
4. Multiply the last terms: \(-1 \times 3 = -3\)

Now combine all these terms:

\[
x^2 + 3x - x - 3
\]

Simplify by combining like terms:

\[
x^2 + 2x - 3
\]

So, the simplified form is:

\[
x^2 + 2x - 3
\]

Would you like a detailed explanation of any part of the process?

Here are 5 related questions you might find interesting:
1. How do you factor a quadratic expression like \(x^2 + 2x - 3\)?
2. What is the importance of the distributive property in algebra?
3. How does the FOIL method apply to binomial multiplication?
4. Can this quadratic expression be solved using the quadratic formula?
5. How can you verify the solution by expanding again?

**Tip:** Always check your simplified expression by expanding it back out to see if you get the original!

This lesson provides a step-by-step guide on how to simplify the expression (x-1)(x+3) using the FOIL method. It covers key algebraic concepts like binomial multiplication and the distributive property, and is suitable for students in Grades 7-9.

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