To factorize the quadratic expression \(2x^2 + 4x + 2\), we can follow these steps:

1. **Identify the common factor:** Notice that each term in the expression has a common factor of 2. We can factor out this common factor first:
   \[
   2x^2 + 4x + 2 = 2(x^2 + 2x + 1).
   \]

2. **Factor the quadratic inside the parentheses:** Now, we need to factorize the quadratic expression \(x^2 + 2x + 1\). This can be written as:
   \[
   x^2 + 2x + 1 = (x + 1)(x + 1) = (x + 1)^2.
   \]

3. **Combine the factors:** Now, substitute back to get the fully factored form:
   \[
   2(x^2 + 2x + 1) = 2(x + 1)^2.
   \]

So, the factorized form of the expression \(2x^2 + 4x + 2\) is:

\[
\boxed{2(x + 1)^2}.
\]

Would you like more details on any of these steps or have any questions?

### Related Questions:
1. How do you factorize a quadratic expression without a common factor?
2. What are the different methods to factorize quadratic equations?
3. How do you complete the square to solve a quadratic equation?
4. Can you explain the significance of the discriminant in factorization?
5. What is the relationship between roots and factors of a quadratic equation?

### Tip:
When factoring a quadratic expression, always start by looking for a common factor among all the terms before applying other factorization techniques.

Learn how to factorize the quadratic expression 2x^2 + 4x + 2 step-by-step. This guide covers factorization techniques, including factoring out the greatest common factor and completing the square. Ideal for students in Grades 7-9.

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