The expression $(a+b)(a+b)$ can be simplified using the distributive property, also known as the FOIL method (First, Outer, Inner, Last):

$(a+b)(a+b) = a(a+b) + b(a+b)$

Now distribute $a$ and $b$ to each term inside the parentheses:

$= a^2 + ab + ba + b^2$

Since $ab$ and $ba$ are the same, they can be combined:

$= a^2 + 2ab + b^2$

So, the simplified form of $(a+b)(a+b)$ is:

$a^2 + 2ab + b^2$

Would you like any more details or have any other questions? Here are some related questions you might find interesting:

1. How do you expand $(a-b)(a+b)$?
2. What is the binomial theorem?
3. How do you factor $a^2 + 2ab + b^2$?
4. How do you solve quadratic equations?
5. Can you explain the distributive property in more detail?

Tip: Always combine like terms to simplify algebraic expressions efficiently.