(a+b)(a+b) can be expanded using the distributive property:
(a+b)(a+b) = a(a+b) + b(a+b)
Using the distributive property again:
= a^2 + ab + ba + b^2
Since multiplication is commutative, ab and ba are the same:
= a^2 + 2ab + b^2
So, (a+b)(a+b) = a^2 + 2ab + b^2.