Step 1 :Julio made an error in the factoring of the quadratic expression inside the parentheses. He factored it as \((x+1)(x+9)\), but this is incorrect. We need to find the correct factorization of the quadratic expression.
Step 2 :First, factor out the common factor of 2 from the expression: \(2x^2 + 12x + 18 = 2(x^2 + 6x + 9)\)
Step 3 :Next, factor the quadratic expression inside the parentheses: \((x^2 + 6x + 9) = (x+3)(x+3)\)
Step 4 :Finally, substitute the correct factorization back into the expression: \(2(x^2 + 6x + 9) = 2(x+3)(x+3)\)
Step 5 :\(\boxed{2(x+3)(x+3)}\) is the correct factorization of \(2x^2 + 12x + 18\)