If a^2 + 2ab + b^2 = 81, then calculate a + b.

First Binomial: a^2 + 2ab + b^2 = (a + b)^2.

 

(a + b)^2  = 81   | \(\sqrt{ }\)

a + b = 9.

 

So \(\boxed{ a + b = 9 }\) .