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.

Learn how to expand the expression (a+c)(a+d) using the distributive property. This detailed solution covers binomial expansion and the use of algebraic formulas to simplify the result. Suitable for students in Grades 8-10.

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