5. $$ x^{2} y^{2}-1 $$ 7. $$ 28 x^{3}-63 x b^{2} $$

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Certainly! It looks like you're working on factoring algebraic expressions. Let's tackle each one step by step.

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**5. $$ x^{2} y^{2} - 1 $$**

This expression is a **difference of squares**, which follows the pattern:

$$
a^2 - b^2 = (a - b)(a + b)
$$

Here, $$ a = xy $$ and $$ b = 1 $$. Applying the pattern:

$$
x^{2} y^{2} - 1 = (xy)^2 - 1^2 = (xy - 1)(xy + 1)
$$

**Factored Form:**

$$
(xy - 1)(xy + 1)
$$

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**7. $$ 28 x^{3} - 63 x b^{2} $$**

First, **factor out the greatest common factor (GCF)** from both terms.

1. **Identify the GCF of the coefficients (28 and 63):**
   - The GCF of 28 and 63 is **7**.

2. **Identify the GCF of the variables:**
   - Both terms have at least **$$ x $$**.
   
   So, the GCF is **$$ 7x $$**.

3. **Factor out the GCF:**
   
$$
28 x^{3} - 63 x b^{2} = 7x (4x^{2} - 9b^{2})
$$

4. **Notice that $$ 4x^{2} - 9b^{2} $$ is also a difference of squares:**
   
$$
4x^{2} - 9b^{2} = (2x)^2 - (3b)^2 = (2x - 3b)(2x + 3b)
$$

5. **Combine the factored forms:**
   
$$
7x (2x - 3b)(2x + 3b)
$$

**Factored Form:**

$$
7x (2x - 3b)(2x + 3b)
$$

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**Summary:**

1. **Expression 5:**  
   $$ x^{2} y^{2} - 1 = (xy - 1)(xy + 1) $$

2. **Expression 7:**  
   $$ 28 x^{3} - 63 x b^{2} = 7x (2x - 3b)(2x + 3b) $$

If you have any more expressions you'd like to factor or any other questions, feel free to ask!
**5. $$ x^{2} y^{2} - 1 $$** $$ (xy - 1)(xy + 1) $$ **7. $$ 28 x^{3} - 63 x b^{2} $$** $$ 7x (2x - 3b)(2x + 3b) $$

5. \( x^{2} y^{2}-1 \) 7. \( 28 x^{3}-63 x b^{2} \)

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