To simplify the expression \((x + 2)(x - 3)\), we can apply the **distributive property** (also known as the FOIL method for binomials):

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

Now, simplify each term:

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

Now combine like terms:

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

So, the simplified form is:

\[
(x + 2)(x - 3) = x^2 - x - 6
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How would you expand \((x - 5)(x + 4)\)?
2. What is the result of \((2x + 3)(x - 1)\)?
3. Can you factor the expression \(x^2 - x - 6\)?
4. How does the distributive property work for more complex polynomials like \((x^2 + x)(x - 1)\)?
5. What happens when you multiply two binomials with the same terms but opposite signs, like \((x + 4)(x - 4)\)?

**Tip**: The FOIL method (First, Outer, Inner, Last) is a great way to remember the distributive property when expanding binomials.

Learn how to simplify the binomial expression (x+2)(x-3) using the distributive property and the FOIL method. This step-by-step guide covers key algebraic concepts like binomial expansion and the distributive property, ideal for students in Grades 8-10.

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