To expand the expression $(A + 2)(A + 3)$, we use 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:

$A^2 + 5A + 6$

So, $(A + 2)(A + 3) = A^2 + 5A + 6$.

Let me know if you'd like more details or further questions!

Related questions:

1. How would you expand $(x - 1)(x + 4)$?
2. What is the difference between expanding binomials and factoring quadratics?
3. Can you factor the expression $A^2 + 5A + 6$ back into binomial form?
4. How do you handle negative numbers when expanding binomials like $(A - 2)(A - 3)$?
5. How do you use the FOIL method for more complex binomials involving coefficients or constants?

Tip: Always group like terms after expanding to simplify the expression effectively.