To expand and simplify \((x + 2)(x - 3)\), apply the distributive property (often called FOIL for binomials):

\[
(x + 2)(x - 3) = x(x) + x(-3) + 2(x) + 2(-3)
\]

Now, simplify each term:

1. \(x \cdot x = x^2\)
2. \(x \cdot (-3) = -3x\)
3. \(2 \cdot x = 2x\)
4. \(2 \cdot (-3) = -6\)

Combine all terms:

\[
x^2 - 3x + 2x - 6
\]

Combine like terms:

\[
x^2 - x - 6
\]

So, the expanded and simplified form is:

\[
x^2 - x - 6
\]

Would you like a detailed breakdown of each step or have any questions?

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Here are some related questions to explore:

1. How do you expand and simplify \((x - 5)(x + 4)\)?
2. How would you expand and simplify \((2x + 3)(x - 1)\)?
3. What is the expanded form of \((x + a)(x + b)\)?
4. How can you verify the expansion by plugging in values for \(x\)?
5. How does the distributive property apply when expanding \((x + y)(x - y)\)?

**Tip:** When expanding two binomials, remember to carefully distribute each term to avoid errors in sign.

Learn how to expand and simplify the expression (x + 2)(x - 3) using the distributive property. This detailed explanation covers key algebraic concepts, including polynomial expansion and simplification. Suitable for students in Grades 7-9.

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