ISCELÁNEA cribir, por simple inspección, el resultado de: \( \begin{array}{lll}(x+2)^{2} & \text { 14. }(x+y+1)(x-y-1) & \text { 27. }\left(2 a^{3}-5 b^{4}\right)^{2} \\ (x+2)(x+3) & \text { 15. }(1-a)(a+1) & \text { 28. }\left(a^{3}+12\right)\left(a^{3}-15\right) \\ (x+1)(x-1) & \text { 16. }(m-8)(m+12) & \text { 29. }\left(m^{2}-m+n\right)\left(n+m+m^{2}\right) \\ (x-1)^{2} & \text { 17. }\left(x^{2}-1\right)\left(x^{2}+3\right) & \text { 30. }\left(x^{4}+7\right)\left(x^{4}-11\right) \\ (n+3)(n+5) & \text { 18. }\left(x^{3}+6\right)\left(x^{3}-8\right) & \text { 31. }(11-a b)^{2} \\ (m-3)(m+3) & \text { 19. }\left(5 x^{3}+6 m^{4}\right)^{2} & \text { 32. }\left(x^{2} y^{3}-8\right)\left(x^{2} y^{3}+6\right) \\ (a+b-1)(a+b+1) & \text { 20. }\left(x^{4}-2\right)\left(x^{4}+5\right) & \text { 33. }(a+b)(a-b)\left(a^{2}-b^{2}\right) \\ (1+b)^{3} & \text { 21. }(1-a+b)(b-a-1) & \text { 34. }(x+1)(x-1)\left(x^{2}-2\right) \\ \left(a^{2}+4\right)\left(a^{2}-4\right) & \text { 22. }\left(a^{x}+b^{n}\right)\left(a^{x}-b^{n}\right) & \text { 35. }(a+3)\left(a^{2}+9\right)(a-3) \\ \left(3 a b-5 x^{2}\right)^{2} & \text { 23. }\left(x^{a+1}-8\right)\left(x^{a+1}+9\right) & \text { 36. }(x+5)(x-5)\left(x^{2}+1\right) \\ (a b+3)(3-a b) & \text { 24. }\left(a^{2} b^{2}+c^{2}\right)\left(a^{2} b^{2}-c^{2}\right) & \text { 37. }(a+1)(a-1)(a+2)(a-2) \\ (1-4 a x)^{2} & \text { 25. }(2 a+x)^{3} & \text { 36. }\left(x^{2}-11\right)\left(x^{2}-2\right)\end{array} \) \( \left(a^{2}+8\right)\left(a^{2}-7\right) \)

A continuación, se presentan los resultados de las expresiones dadas, escritas por simple inspección: 1. \( (x+2)^{2} = x^{2} + 4x + 4 \) 2. \( (x+2)(x+3) = x^{2} + 5x + 6 \) 3. \( (x+1)(x-1) = x^{2} - 1 \) 4. \( (x-1)^{2} = x^{2} - 2x + 1 \) 5. \( (n+3)(n+5) = n^{2} + 8n + 15 \) 6. \( (m-3)(m+3) = m^{2} - 9 \) 7. \( (a+b-1)(a+b+1) = (a+b)^{2} - 1 \) 8. \( (1+b)^{3} = 1 + 3b + 3b^{2} + b^{3} \) 9. \( \left(a^{2}+4\right)\left(a^{2}-4\right) = a^{4} - 16 \) 10. \( \left(3ab-5x^{2}\right)^{2} = 9a^{2}b^{2} - 30abx^{2} + 25x^{4} \) 11. \( (a b+3)(3-a b) = 3ab - a^{2}b^{2} + 9 \) 12. \( (1-4ax)^{2} = 1 - 8ax + 16a^{2}x^{2} \) 13. \( (2a+x)^{3} = 8a^{3} + 12a^{2}x + 6ax^{2} + x^{3} \) 14. \( (x^{2}-11)(x^{2}-2) = x^{4} - 13x^{2} + 22 \) 15. \( (x+y+1)(x-y-1) = x^{2} + (y-1)x + (y-1) \) Continuando con las demás expresiones: 16. \( (1-a)(a+1) = -a^{2} + 1 \) 17. \( (m-8)(m+12) = m^{2} + 4m - 96 \) 18. \( \left(x^{2}-1\right)\left(x^{2}+3\right) = x^{4} + 2x^{2} - 3 \) 19. \( \left(x^{3}+6\right)\left(x^{3}-8\right) = x^{6} - 2x^{3} - 48 \) 20. \( (5x^{3}+6m^{4})^{2} = 25x^{6} + 60x^{3}m^{4} + 36m^{8} \) 21. \( (x^{4}-2)(x^{4}+5) = x^{8} + 3x^{4} - 10 \) 22. \( (a^{x}+b^{n})(a^{x}-b^{n}) = a^{2x} - b^{2n} \) 23. \( (x^{a+1}-8)(x^{a+1}+9) = x^{2(a+1)} + x^{a+1} - 72 \) 24. \( (a^{2}b^{2}+c^{2})(a^{2}b^{2}-c^{2}) = a^{4}b^{4} - c^{4} \) 25. \( (x+5)(x-5)(x^{2}+1) = (x^{2}-25)(x^{2}+1) = x^{4} - 24x^{2} - 25 \) 26. \( (a+1)(a-1)(a+2)(a-2) = (a^{2}-1)(a^{2}-4) = a^{4} - 5a^{2} + 4 \) Finalmente, para la expresión \( \left(a^{2}+8\right)\left(a^{2}-7\right) \): 27. \( \left(a^{2}+8\right)\left(a^{2}-7\right) = a^{4} + a^{2} - 56 \) Estos son los resultados de las expresiones dadas.