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.