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Let's go through the three questions from the quiz.

### Question 1: Factor \( 8x^2 - 50 \)

This is a difference of squares. It can be factored as follows:

\[
8x^2 - 50 = 2(4x^2 - 25) = 2(2x - 5)(2x + 5)
\]

### Factored form: \( 2(2x - 5)(2x + 5) \)

---

### Question 2: Factor \( 4x^2 - 16x + 16 \)

This is a perfect square trinomial. It can be factored as follows:

\[
4x^2 - 16x + 16 = (2x - 4)^2
\]

### Factored form: \( (2x - 4)^2 \) or \( (2(x - 2))^2 = 4(x - 2)^2 \)

---

### Question 3: Factor \( 4x^3 - 108 \)

Factor out the greatest common factor first, and then factor the difference of cubes:

\[
4x^3 - 108 = 4(x^3 - 27) = 4(x - 3)(x^2 + 3x + 9)
\]

### Factored form: \( 4(x - 3)(x^2 + 3x + 9) \)

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Would you like further details or clarifications on these solutions?

Here are some follow-up questions to deepen understanding:
1. What are the conditions for factoring as a difference of squares?
2. How do you identify a perfect square trinomial?
3. Can a sum of cubes be factored similarly to a difference of cubes?
4. How does factoring help in solving quadratic equations?
5. What are the steps involved in factoring polynomials with common factors?

**Tip**: Always look for common factors before trying other factoring techniques—it simplifies the problem!

Factor the following expressions: 8x^2 - 50, 4x^2 - 16x + 16, and 4x^3 - 108

Learn how to factor algebraic expressions such as 8x^2 - 50, 4x^2 - 16x + 16, and 4x^3 - 108 with detailed step-by-step solutions. This problem covers key algebraic concepts like the difference of squares, perfect square trinomials, and the difference of cubes. Suitable for students in Grades 9-11.

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