1. The problem asks to simplify the expression $$(a - b)^2 + 4ab$$. 2. Recall the formula for the square of a binomial: $$(a - b)^2 = a^2 - 2ab + b^2$$. 3. Substitute this into the expression: $$ (a - b)^2 + 4ab = (a^2 - 2ab + b^2) + 4ab $$ 4. Combine like terms: $$ a^2 - 2ab + b^2 + 4ab = a^2 + ( -2ab + 4ab ) + b^2 = a^2 + 2ab + b^2 $$ 5. Recognize that this is the expansion of $$(a + b)^2$$. 6. Therefore, the simplified expression is: $$ (a + b)^2 $$ 7. The correct answer is option C.