1. The problem is to simplify the expression $$(x + 4)^2 + 3(x + 4)$$. 2. Use the formula for the square of a binomial: $$(a + b)^2 = a^2 + 2ab + b^2$$. 3. Apply the formula to $$(x + 4)^2$$: $$x^2 + 2 \cdot x \cdot 4 + 4^2 = x^2 + 8x + 16$$. 4. Now add the term $$3(x + 4)$$: $$3x + 12$$. 5. Combine all terms: $$x^2 + 8x + 16 + 3x + 12$$. 6. Simplify by combining like terms: $$x^2 + (8x + 3x) + (16 + 12) = x^2 + 11x + 28$$. 7. The simplified expression is $$x^2 + 11x + 28$$.