Match each expression with its correct factorization.
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Part 1
Use the choices below to fill in each blank.

1. x squared minus y squaredx2−y2equals=
2. x cubed minus y cubedx3−y3equals=
3. x cubed plus y cubedx3+y3equals=
4. x squared plus 2 xy plus y squaredx2+2xy+y2equals=

Let's go through each expression and match it with its correct factorization.

1. **\( x^2 - y^2 \)**  
   This is a difference of squares, which can be factored as:
   \[
   x^2 - y^2 = (x + y)(x - y)
   \]

2. **\( x^3 - y^3 \)**  
   This is a difference of cubes, which can be factored as:
   \[
   x^3 - y^3 = (x - y)(x^2 + xy + y^2)
   \]

3. **\( x^3 + y^3 \)**  
   This is a sum of cubes, which can be factored as:
   \[
   x^3 + y^3 = (x + y)(x^2 - xy + y^2)
   \]

4. **\( x^2 + 2xy + y^2 \)**  
   This is a perfect square trinomial, which can be factored as:
   \[
   x^2 + 2xy + y^2 = (x + y)^2
   \]

### Summary:
- \( x^2 - y^2 = (x + y)(x - y) \)
- \( x^3 - y^3 = (x - y)(x^2 + xy + y^2) \)
- \( x^3 + y^3 = (x + y)(x^2 - xy + y^2) \)
- \( x^2 + 2xy + y^2 = (x + y)^2 \)

Would you like further clarification or examples?

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**Related Questions:**

1. How do you factor \( x^4 - y^4 \)?
2. What is the factorization of \( x^2 + y^2 \)?
3. Can \( x^2 - 4xy + 4y^2 \) be factored as a perfect square?
4. How do you recognize a sum of cubes versus a difference of cubes?
5. How can you expand \( (x - y)^2 \) to verify its factors?

**Tip:** Remember, differences of squares, cubes, and perfect squares have specific patterns that simplify factorization!

Match each expression with its correct factorization. 1. x^2 - y^2 equals= 2. x^3 - y^3 equals= 3. x^3 + y^3 equals= 4. x^2 + 2xy + y^2 equals=

Learn to factor expressions like x^2 - y^2, x^3 - y^3, x^3 + y^3, and x^2 + 2xy + y^2 with detailed examples covering key algebraic concepts. This guide is ideal for students in Grades 9-10, focusing on differences of squares, cubes, and perfect square trinomials.

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