1. (3p + 5)(p - 1)
2. 3(x - 5)(x + 3)
3. (4w + 5)(w - 5)
4. (2y - 5)²
5. 10j(j - 4)(j - 10)
6. -(4b - 7)(b - 7)
7. (2n + m)(n + 2m)
8. (4y - 1)(y - 4)
9. -(5x - 3)(x - 3)
10. 4(3u² - u - 4) = 4(3u - 4)(u + 1)
11. z²(z + 7)(z - 1)
12. 3(3k + 1)²
13. (3x + y)(2x - 3y)
14. 3(2b + 1)(b - 3)
15. (4w + 3)(w - 5)
16. (4y - 5)(y - 3)
17. 3m(5m² + 3m - 2) = 3m(5m - 2)(m + 1)
18. (z + 1)²(z - 1)
19. (h - k)(h² + hk + k²)
20. r(8p³ + r³) = r(2p + r)(4p² - 2pr + r²)
21. 25h³(5h - 3)(25h² + 15h + 9)
22. (3c - 2d)(9c⁴ + 6c³d + 4c²d² + 2cd³ + d⁴) [Note: This is not a standard difference of cubes; it's c⁵ - d⁵ factored as (c - d)(c⁴ + c³d + c²d² + cd³ + d⁴), but here it's 27c⁵ - 8d⁵ = (3c)⁵ - (2d)⁵, which factors as (3c - 2d)((3c)⁴ + (3c)³(2d) + (3c)²(2d)² + (3c)(2d)³ + (2d)⁴)]
23. 2b³(125a³ + 1) = 2b³(5a + 1)(25a² - 5a + 1)
24. (6w - 7z)(6w + 7z)
25. 5(x - 3)(x + 3)
26. a³x(1 - 16a²) = a³x(1 - 4a)(1 + 4a)
27. (4a² - b²)(4a² + b²) = (2a - b)(2a + b)(4a² + b²)
28. 3x²(x + 6)²
29. (2u + 5)²
30. (11b - 3d)²
Parent Tip: Review the logic above to help your child master the concept of factoring algebra 2 worksheet.
