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

Certainly! It looks like you're working on factoring algebraic expressions. Let's tackle each one step by step. --- **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:** \[ (xy - 1)(xy + 1) \] --- **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:** \[ 7x (2x - 3b)(2x + 3b) \] --- **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!