1. Factor the following: 25x² - 49y²

Answer:
= (5x)² - (7y)²
= (5x + 7y)(5x - 7y)


2. Factor the following: m³ - 8n³

Answer:
= m³ - (2n)³ = (m - 2n)[m² + m(2n) + (2n)²
= (m - 2n)(m² + 2mn + 4n²)


3. Factor the following: 27a³ + 64b³

Answer:
= (3a)³ + (4b)³
= (3a + 4b)[(3a)² - 3a(4b) + (4b)²]
= (3a + 4b)(9a² - 12ab + 16b²)


4. Factor the following: 8x⁶ - 64y⁹

Answer:
= (2x²)³ - (4y³)³
= (2x² - 4y³)[(2x²)² + (2x²)(4y³) + (4y³)²]
= (2x² - 4y³)(4x⁴ + 8x²y³ + 16y⁶)


5. Factor the following: 27x³ + 125y⁶

Answer:
= (3x)³ + (5y²)³
= (3x + 5y²)[(3x)² - 3x(5y²) + (5y²)²]
= (3x + 5y²)(9x² - 15xy² + 5y⁴)