Dưới đây là phân tích các đa thức thành nhân tử hoặc hằng đẳng thức:

1. (a²-4b² = (a-2b)(a+2b))
2. (4a²-b² = (2a-b)(2a+b))
3. (25a^4 - 1 = (5a2-1)(5a2+1))
4. ((a + b)² - 4 = (a+b-2)(a+b+2))
5. (25b^2 - (2-5b)^2 = (5b-(2-5b))(5b+(2-5b)))
6. (9 (a² − 2b)² - 16b² = (3(a²-2b)-4b)(3(a²-2b)+4b))
7. ((a-5b)^2 - (2a+5b)^2 = ((a-5b)-(2a+5b))((a-5b)+(2a+5b)))
8. (x^2 + 10x + 25 = (x+5)^2)
9. (x² + 8x + 16 = (x+4)^2)
10. (9x^2 + 12xy + 4y^2 = (3x+2y)^2)
11. (4x^4 + 20x^2 + 25 = (2x2+5)2)
12. (4x² - 12xy +9y² = (2x-3y)^2)
13. (25x^2 - 10xy + 4y^2 = (5x-2y)^2)
14. (25x^2 -10xy +y^2 = (5x-y)^2)
15. (9x^4 - 12x²y + 4y² = (3x2-2y)2)
16. (x^3 + 27x^3 = 28x^3)
17. (8x^3 + y^3 = (2x+y)((2x)2-(2x)y+y2))
18. (64x³ + 8y³ = 8(8x³+y³) = 8((2x+y)((2x)2-(2x)y+y2)))
19. (64x^6 + 1 = (8x3+1)(64x6-8x^3+1))
20. (27 + (x-2)^3 = ((3+(x-2))((3-(x-2))^2+3*(x-2)+1))
21. ((x - 5)³ + (x + 2)² = x3-15x2+75x-125+x^2+4x+4 = x3-14x2+79x-121)
22. (x^3 – 64y^3 = (x-4y)(x2+4xy+16y2))
23. (125x^3 - y^3 = (5x-y)(25x2+5xy+y2))
24. (27x^3 - 8y^3 = (3x-2y)(9x2+6xy+4y2))