To expand the expression $(a+c)(a+d)$, we can apply the distributive property (also known as FOIL for binomials):

$(a+c)(a+d) = a(a+d) + c(a+d)$

Now, distribute $a$ and $c$ across the terms inside the parentheses:

$a(a+d) = a^2 + ad$ $c(a+d) = ca + cd$

Now, combine all the terms:

$a^2 + ad + ca + cd$

This is the expanded form of $(a+c)(a+d)$:

$a^2 + ad + ca + cd$

Would you like further details or have any questions?

Related Questions:

1. How would the expansion change if $a = 1$, $c = 2$, and $d = 3$?
2. Can you expand $(a+b)(a+d)$ and compare with the current result?
3. How would you factor the expression $a^2 + ad + ca + cd$?
4. What is the geometric interpretation of this expansion?
5. How does the distributive property apply to expressions with more variables?

Tip: Always combine like terms after expanding expressions to simplify the result.