https://file.aiquickdraw.com/mathbot/file/17257554777698i4lk69f.jpg

The problem displayed in the image is:

**Question 5:**

Simplify the expression \( 8x^2 + 8x + 2 \) and choose the correct factorization among the given options.

Let's begin by factoring the quadratic expression:

### Step 1: Identify the common factor
The expression is:
\[
8x^2 + 8x + 2
\]
Notice that each term has a factor of 2. We can factor out 2:
\[
2(4x^2 + 4x + 1)
\]

### Step 2: Factor the quadratic inside the parentheses
Now, we need to factor the quadratic expression \( 4x^2 + 4x + 1 \). This is a perfect square trinomial, which factors as:
\[
4x^2 + 4x + 1 = (2x + 1)^2
\]

### Step 3: Combine the factored terms
Substituting this back into the expression, we have:
\[
2(2x + 1)^2
\]

### Conclusion:
The correct factorization is \( 2(2x + 1)^2 \).

Thus, the correct option in the image is the third one, which shows \( 2(2x + 1)^2 \).

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Would you like any further details or explanations?

Here are some related questions to expand your understanding:
1. How do you determine if a trinomial is a perfect square?
2. What are some techniques for factoring quadratic expressions that are not perfect squares?
3. Can this factorization method be applied to higher-degree polynomials?
4. How would you graph \( 8x^2 + 8x + 2 \) and its factored form?
5. What role does the discriminant play in identifying the nature of quadratic roots?

**Tip:** Always check if the quadratic can be factored by identifying common factors first before using more complex methods like completing the square or the quadratic formula.

Simplify the expression 8x^2 + 8x + 2 and choose the correct factorization among the given options.

Learn how to factor the quadratic expression 8x^2 + 8x + 2 step-by-step. This problem demonstrates how to identify perfect square trinomials and factor quadratic equations. Suitable for students in Grades 9-11.

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