4. Julio was asked to factor the expression $2 x^{2}+12 x+18$. His solution is shown below:
\[
\begin{aligned}
2 x^{2}+12 x+18 & =2\left(x^{2}+10 x+9\right) \\
& =2(x+1)(x+9)
\end{aligned}
\]
(1 mark)
a. Identify the error that Julio made.
(2 marks)
b. Determine the correct factorization of $2 x^{2}+12 x+18$

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 \(2x^2 + 12x + 18\)