https://file.aiquickdraw.com/mathbot/file/1725970108231vifr1dqh.jpg

The image contains a list of polynomials, and the task is to identify whether each is a perfect square trinomial, a difference of squares, or a sum or difference of two cubes. Let's go through each one:

1. **\( x^2 - 121 \)**

   - This is a **difference of squares**: \( x^2 - 121 = x^2 - 11^2 = (x - 11)(x + 11) \).

2. **\( 27x^3 + 1 \)**

   - This is a **sum of cubes**: \( 27x^3 + 1 = (3x)^3 + 1^3 = (3x + 1)(9x^2 - 3x + 1) \).

3. **\( x^6 - y^2 \)**

   - This can be seen as a **difference of squares**: \( x^6 - y^2 = (x^3 - y)(x^3 + y) \).

4. **\( x^2 + 8x + 16 \)**

   - This is a **perfect square trinomial**: \( x^2 + 8x + 16 = (x + 4)^2 \).

5. **\( 4x^2 - 4xy + y^2 \)**

   - This is a **perfect square trinomial**: \( 4x^2 - 4xy + y^2 = (2x - y)^2 \).

6. **\( (x - 0.001y)^3 \)**

   - This is a **cube**: \( (x - 0.001y)^3 \) is already in a factored form of a cube.

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

Here are five related questions:

1. How do you factor a difference of cubes?
2. What are the characteristics of a perfect square trinomial?
3. How do you identify whether a polynomial is a difference of squares?
4. Can a sum of cubes be factored similarly to a sum of squares?
5. What are some examples of polynomials that cannot be factored using simple algebraic identities?

**Tip:** When factoring polynomials, always check for common factors first before applying specific identities like difference of squares or cubes.

Identify the polynomial if it is a perfect square trinomial, a difference of squares, or a sum or difference of two cubes.

Learn how to identify and factor different types of polynomials, including perfect square trinomials, differences of squares, and sums or differences of cubes. This lesson is ideal for high school students in Grades 9-12.

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