11. \( x^{12} - y^4 \)

\[ x^{12} - y^4 = (x^6 - y^2)(x^6 + y^2) \]

12. \( x^3 + 3x^2 + 3x + 1 \)

\[ x^3 + 3x^2 + 3x + 1 = (x+1)^3 \]

13. \( \frac{1}{25} - 36x^2 \)

\[ \frac{1}{25} - 36x^2 = \frac{1 - 900x^2}{25} \]

14. \( (a-2b)^2 - 4b^2 \)

\[ (a-2b)^2 - 4b^2 = (a^2 - 4ab + 4b^2) - 4b^2 = a^2 - 4ab \]

15. \( 25a^2 - (a-b)^2 \)

\[ 25a^2 - (a-b)^2 = 25a^2 - (a^2 - 2ab + b^2) = 24a^2 + 2ab - b^2 \]

16. \( 36a^2 - (3a-2b)^2 \)

\[ 36a^2 - (3a-2b)^2 = 36a^2 - (9a^2 - 12ab + 4b^2) = 36a^2 - 9a^2 + 12ab - 4b^2 = 27a^2 + 12ab - 4b^2 \]

17. \( (5a-b)^2 - (2a+3b)^2 \)

\[ (5a-b)^2 - (2a+3b)^2 = (25a^2 - 10ab + b^2) - (4a^2 + 12ab + 9b^2) = 21a^2 - 22ab - 8b^2 \]

18. \( (2a-b)^2 - 4(a-b)^2 \)

\[ (2a-b)^2 - 4(a-b)^2 = (4a^2 - 4ab + b^2) - 4(a^2 - 2ab + b^2) = 4a^2 - 4ab + b^2 - 4a^2 + 8ab - 4b^2 = 4ab - 3b^2 \]

19. \( 49(x-5)^2 - (x+4)^2 \)

\[ 49(x-5)^2 - (x+4)^2 = 49(x^2 - 10x + 25) - (x^2 + 8x + 16) = 49x^2 - 490x + 1225 - x^2 - 8x - 16 = 48x^2 - 498x + 1209 \]

20. \( 36(x-t)^2 - 25(2x-1)^2 \)

\[ 36(x-t)^2 - 25(2x-1)^2 = 36(x^2 - 2xt + t^2) - 25(4x^2 - 4x + 1) = 36x^2 - 72xt + 36t^2 - 100x^2 + 100x - 25 \]

21. \( x^2 + 8x + 16 \)

\[ x^2 + 8x + 16 = (x + 4)^2 \]

22. \( 4x^2 + 12x + 9 \)

\[ 4x^2 + 12x + 9 = (2x + 3)^2 \]

23. \( 9x^4 + 24x^2 + 16 \)

\[ 9x^4 + 24x^2 + 16 = (3x^2 + 4)^2 \]

24. \( 4x^2 - 12xy + 9y^2 \)

\[ 4x^2 - 12xy + 9y^2 = (2x - 3y)^2 \]

25. \( 9x^4 - 12x^3 + 4x^2 \)

\[ 9x^4 - 12x^3 + 4x^2 = x^2(9x^2 - 12x + 4) \]

Khai triển các hằng đẳng thức:

1) \((a-5b)^2 - 16b^2\)
\[
(a-5b+4b)(a-5b-4b) = (a - b)(a - 9b)
\]

2) \(49a^2 - (2a - b)^2\)
\[
(7a + (2a - b))(7a - (2a - b)) = (9a - b)(5a + b)
\]

3) \((4a + 3b)^2 - (b - 2a)^2\)
\[
(4a + 3b + b - 2a)(4a + 3b - (b - 2a)) = (6a + 4b)(6a + 2b)
\]

4) \(9(a + b)^2 - 4(a - 2b)^2\)
\[
(3(a + b) + 2(a - 2b))(3(a + b) - 2(a - 2b)) = (5a - b)(a + 7b)
\]

5) \(4x^4 + 20x^2 + 25\)
\[
(2x^2 + 5)^2
\]

6) \(25x^2 - 20xy + 4y^2\)
\[
(5x - 2y)^2
\]

7) \(x^{10} - 4x^8 + 4x^6\)
\[
x^6(x^4 - 4x^2 + 4) = x^6(x^2 - 2)^2
\]

8) \(m^3 + 27\)
\[
(m + 3)(m^2 - 3m + 9)
\]

9) \(125 - (x + 2)^3\)
\[
(5 - (x + 2))(25 + 5(x + 2) + (x + 2)^2)
\]

10) \((x - 5)^3 - 27\)
\[
(x - 5 - 3)((x - 5)^2 + 3(x - 5) + 9) = (x - 8)(x^2 - 7x + 19)
\]

11) \(x^{12} - y^4\)
\[
(x^6 - y^2)(x^6 + y^2) = (x^2 - y)(x^2 + y)(x^4 + y^2)(x^4 - x^2y + y^2)
\]

12) \(x^3 + 3x^2 + 3x + 1\)
\[
(x + 1)^3
\]

13) \(\frac{1}{25} - 36x^2\)
\[
(\frac{1}{5} - 6x)(\frac{1}{5} + 6x)
\]

14) \((a - 2b)^2 - 4b^2\)
\[
((a - 2b) + 2b)((a - 2b) - 2b) = a(a - 4b)
\]

15) \(25a^2 - (a - b)^2\)
\[
(5a + (a - b))(5a - (a - b)) = (6a - b)(4a + b)
\]

16) \(36a^2 - (3a - 2b)^2\)
\[
(6a + (3a - 2b))(6a - (3a - 2b)) = (9a + 2b)(3a - 2b)
\]

17) \((5a - b)^2 - (2a + 3b)^2\)
\[
((5a - b) + (2a + 3b))((5a - b) - (2a + 3b)) = (7a + 2b)(3a - 4b)
\]

18) \((2a - b)^2 - 4(a - b)^2\)
\[
(2a - b + 2(a - b))(2a - b - 2(a - b)) = (4a - 3b)(2a + b)
\]

19) \(49(x - 5)^2 - (x + 4)^2\)
\[
(7(x - 5) + (x + 4))(7(x - 5) - (x + 4)) = (8x - 31)(6x - 39)
\]

20) \(36(x - t)^2 - 25(2x - 1)^2\)
\[
(6(x - t) + 5(2x - 1))(6(x - t) - 5(2x - 1)) = (16x - 6t - 5)(-4x + 6t + 5)
\]

21) \(x^2 + 8x + 16\)
\[
(x + 4)^2
\]

22) \(4x^2 + 12x + 9\)
\[
(2x + 3)^2
\]

23) \(9x^4 + 24x^2 + 16\)
\[
(3x^2 + 4)^2
\]

24) \(4x^2 - 12xy + 9y^2\)
\[
(2x - 3y)^2
\]

25) \(9x^4 - 12x^7 + 4x^8\)
\[
x^4(9 - 12x^3 + 4x^4)
\]

26) \(8x^3 + 27y^3\)
\[
(2x + 3y)(4x^2 - 6xy + 9y^2)
\]

27) \(8x^6 + 27y^3\)
\[
(2x^2 + 3y)(4x^4 - 6x^2y + 9y^2)
\]

28) \(\frac{1}{64}x^6 - 125y^3\)
\[
(\frac{1}{4}x^2 - 5y)(\frac{1}{16}x^4 + \frac{5}{4}x^2y + 25y^2)
\]

29) \(x^3 - (y - 1)^3\)
\[
(x - (y - 1))(x^2 + x(y - 1) + (y - 1)^2) = (x - y + 1)(x^2 + xy - x + y^2 - 2y + 1)
\]

30) \((x + 3)^3 - 125\)
\[
((x + 3) - 5)((x + 3)^2 + 5(x + 3) + 25) = (x - 2)(x^2 + 11x + 64)
\]

31) \(x^6 - y^6\)
\[
(x^2 - y^2)(x^4 + x^2y^2 + y^4) = (x - y)(x + y)(x^4 + x^2y^2 + y^4)
\]

32) \(x^3 + 6x^2 + 12x + 8\)
\[
(x + 2)^3
\]

33) \(x^3 + 15x^2 + 75x + 125\)
\[
(x + 5)^3
\]

34) \(m^3 - 6m^2 + 12m^2 - m^3\)
\[
6m^2 + 12m^2 = 18m^2
\]

35) \(8a^3 + 12a^2 + 1\)
\[
(2a + 1)(4a^2 - 2a + 1)
\]

36) \(64 - 48m + 12m^2 - m^3\)
\[
(4 - m)(16 + 4m + m^2)
\]

37) \(27a^3 - 27a^2 + 9a - 1\)
\[
(3a - 1)^3
\]

38) \(8a^3 - 12a^2 + 6a - 1\)
\[
(2a - 1)^3
\]

39) \(81a^2 - (5a - 3b)^2\)
\[
(9a + (5a - 3b))(9a - (5a - 3b)) = (14a - 3b)(4a + 3b)
\]

40) \(\frac{4}{9}a^3 - \frac{25}{4}\)
\[
(\frac{2}{3}a - \frac{5}{2})(\frac{4}{9}a^2 + \frac{10}{3}a + \frac{25}{4})
\]