The expression \( 2x^2 - 8x + 4 \) is a quadratic function. If you want to simplify or solve it, I can assist with various methods, such as factoring, completing the square, or using the quadratic formula. Let's break it down:

### Simplifying the Expression:
The greatest common factor (GCF) of all the terms is 2. Let's factor that out first:

\[
2(x^2 - 4x + 2)
\]

Now, the expression is simplified, but it cannot be factored further using simple factorization. 

### Solving the Equation \( 2x^2 - 8x + 4 = 0 \):
If you're looking to solve this quadratic equation, we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For the equation \( 2x^2 - 8x + 4 = 0 \), the coefficients are:
- \( a = 2 \)
- \( b = -8 \)
- \( c = 4 \)

Now, applying these values to the quadratic formula:

\[
x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(2)(4)}}{2(2)}
\]
\[
x = \frac{8 \pm \sqrt{64 - 32}}{4}
\]
\[
x = \frac{8 \pm \sqrt{32}}{4}
\]
\[
x = \frac{8 \pm 4\sqrt{2}}{4}
\]
\[
x = 2 \pm \sqrt{2}
\]

Thus, the two solutions are:

\[
x = 2 + \sqrt{2} \quad \text{or} \quad x = 2 - \sqrt{2}
\]

Would you like more details on any specific step or clarification?

### Related Questions:
1. How do you complete the square for \( 2x^2 - 8x + 4 \)?
2. Can you graph the function \( y = 2x^2 - 8x + 4 \)?
3. What are the applications of solving quadratic equations?
4. Can you explain how to approximate \( \sqrt{2} \) for practical calculations?
5. What are the properties of the parabola represented by \( y = 2x^2 - 8x + 4 \)?

### Tip:
When solving quadratic equations, always check whether factoring is possible before applying the quadratic formula—it can save time!

Explore how to solve the quadratic equation 2x^2 - 8x + 4 using factoring and the quadratic formula. This step-by-step guide covers key algebraic concepts, including factoring and solving quadratic equations, and is ideal for students in Grades 8-10.

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