(x + 1)2 = (x + 1)(x + 1)
Multiply each item in the first set of parenthesees by each item in the second set of parenthesees.
(x + 1)(x + 1) = (x)(x) + (x)(1) + (1)(x) + (1)(1)
Simplify.
(x)(x) + (x)(1) + (1)(x) + (1)(1) = x2 + 2x + 1
So....
(x + 1)2 = x2 + 2x + 1