To expand the expression $(A + 2)(A + 3)$, we apply the distributive property (also known as FOIL for binomials):

$(A + 2)(A + 3) = A(A + 3) + 2(A + 3)$

Now, distribute each term:

$A(A + 3) = A^2 + 3A$ $2(A + 3) = 2A + 6$

Now combine all terms:

$A^2 + 3A + 2A + 6$

Simplify the like terms:

$A^2 + 5A + 6$

So, the expanded form is:

$A^2 + 5A + 6$

Let me know if you'd like further details or have any questions! Here's a list of related questions:

1. What is the result of expanding $(A + 1)(A + 4)$?
2. How can you factor the quadratic expression $A^2 + 5A + 6$?
3. What is the difference between expanding binomials and factoring them?
4. Can you explain the FOIL method in more detail?
5. How do you expand binomials when there are more than two terms?

Tip: Always look for like terms when combining the results of distributing, as it helps simplify the final expression!