Factorizar o descomponer en dos factores: 1. x²-y² 2. a²-1 3. a²-4 4. 9-b² 5. 1-4m² 6. 16-n² 7. a²-25 8. 1-y² 9. 4a²-9 10. 25-36x⁴ 11. 1-49a²b² 12. 4x²-81y⁴ 13. a²b⁸-c² 14. 100-x²y... Factorizar o descomponer en dos factores: 1. x²-y² 2. a²-1 3. a²-4 4. 9-b² 5. 1-4m² 6. 16-n² 7. a²-25 8. 1-y² 9. 4a²-9 10. 25-36x⁴ 11. 1-49a²b² 12. 4x²-81y⁴ 13. a²b⁸-c² 14. 100-x²y⁶ 15. a¹⁰-49b¹² 16. 25x²y⁴-121 17. 100m²n⁴-169y⁶ 18. a²m⁴n⁶-144 19. 196x²y⁴-225z¹² 20. 256a¹²-289b⁴m¹⁰ 21. 1-9a²b⁴c⁶d⁸ Read more

Steps to Solve

1. Recognize the difference of squares pattern

The difference of squares factorization pattern is $a^2 - b^2 = (a + b)(a - b)$. We need to identify $a$ and $b$ in each given expression and apply the pattern.

2. Factor $x^2 - y^2$

Here, $a = x$ and $b = y$. Therefore, $x^2 - y^2 = (x + y)(x - y)$.

3. Factor $a^2 - 1$

Here, $a = a$ and $b = 1$. Therefore, $a^2 - 1 = (a + 1)(a - 1)$.

4. Factor $a^2 - 4$

Here, $a = a$ and $b = 2$. Therefore, $a^2 - 4 = (a + 2)(a - 2)$.

5. Factor $9 - b^2$

Here, $a = 3$ and $b = b$. Therefore, $9 - b^2 = (3 + b)(3 - b)$.

6. Factor $1 - 4m^2$

Here, $a = 1$ and $b = 2m$. Therefore, $1 - 4m^2 = (1 + 2m)(1 - 2m)$.

7. Factor $16 - n^2$

Here, $a = 4$ and $b = n$. Therefore, $16 - n^2 = (4 + n)(4 - n)$.

8. Factor $a^2 - 25$

Here, $a = a$ and $b = 5$. Therefore, $a^2 - 25 = (a + 5)(a - 5)$.

9. Factor $1 - y^2$

Here, $a = 1$ and $b = y$. Therefore, $1 - y^2 = (1 + y)(1 - y)$.

10. Factor $4a^2 - 9$

Here, $a = 2a$ and $b = 3$. Therefore, $4a^2 - 9 = (2a + 3)(2a - 3)$.

11. Factor $25 - 36x^4$

Here, $a = 5$ and $b = 6x^2$. Therefore, $25 - 36x^4 = (5 + 6x^2)(5 - 6x^2)$.

12. Factor $1 - 49a^2b^2$

Here, $a = 1$ and $b = 7ab$. Therefore, $1 - 49a^2b^2 = (1 + 7ab)(1 - 7ab)$.

13. Factor $4x^2 - 81y^4$

Here, $a = 2x$ and $b = 9y^2$. Therefore, $4x^2 - 81y^4 = (2x + 9y^2)(2x - 9y^2)$.

14. Factor $a^2b^8 - c^2$

Here, $a = ab^4$ and $b = c$. Therefore, $a^2b^8 - c^2 = (ab^4 + c)(ab^4 - c)$.

15. Factor $100 - x^2y^6$

Here, $a = 10$ and $b = xy^3$. Therefore, $100 - x^2y^6 = (10 + xy^3)(10 - xy^3)$.

16. Factor $a^{10} - 49b^{12}$

Here, $a = a^5$ and $b = 7b^6$. Therefore, $a^{10} - 49b^{12} = (a^5 + 7b^6)(a^5 - 7b^6)$.

17. Factor $25x^2y^4 - 121$

Here, $a = 5xy^2$ and $b = 11$. Therefore, $25x^2y^4 - 121 = (5xy^2 + 11)(5xy^2 - 11)$.

18. Factor $100m^2n^4 - 169y^6$

Here, $a = 10mn^2$ and $b = 13y^3$. Therefore, $100m^2n^4 - 169y^6 = (10mn^2 + 13y^3)(10mn^2 - 13y^3)$.

19. Factor $a^2m^4n^6 - 144$

Here, $a = am^2n^3$ and $b = 12$. Therefore, $a^2m^4n^6 - 144 = (am^2n^3 + 12)(am^2n^3 - 12)$.

20. Factor $196x^2y^4 - 225z^{12}$

Here, $a = 14xy^2$ and $b = 15z^6$. Therefore, $196x^2y^4 - 225z^{12} = (14xy^2 + 15z^6)(14xy^2 - 15z^6)$.

21. Factor $256a^{12} - 289b^4m^{10}$

Here, $a = 16a^6$ and $b = 17b^2m^5$. Therefore, $256a^{12} - 289b^4m^{10} = (16a^6 + 17b^2m^5)(16a^6 - 17b^2m^5)$.

22. Factor $1 - 9a^2b^4c^6d^8$

Here, $a = 1$ and $b = 3ab^2c^3d^4$. Therefore, $1 - 9a^2b^4c^6d^8 = (1 + 3ab^2c^3d^4)(1 - 3ab^2c^3d^4)$.