在数学学习中，因式分解是一项非常重要的技能。它不仅能够帮助我们简化复杂的代数表达式，还能为后续的学习奠定坚实的基础。为了让大家更好地掌握这一技巧，这里整理了100道因式分解练习题，并附上了详细的答案解析。
练习题部分
1. x^2 - 4
2. x^2 - 9
3. x^2 - 16
4. x^2 - 25
5. x^2 - 36
6. x^2 - 49
7. x^2 - 64
8. x^2 - 81
9. x^2 - 100
10. x^2 - 121
...
（此处省略中间题目）
51. 2x^2 + 10x + 12
52. 3x^2 + 15x + 18
53. 4x^2 + 20x + 24
54. 5x^2 + 25x + 30
55. 6x^2 + 30x + 36
56. 7x^2 + 35x + 42
57. 8x^2 + 40x + 48
58. 9x^2 + 45x + 54
59. 10x^2 + 50x + 60
60. 11x^2 + 55x + 66
...
（此处省略中间题目）
101. 4x^2 - 16x + 16
102. 9x^2 - 36x + 36
103. 16x^2 - 64x + 64
104. 25x^2 - 100x + 100
105. 36x^2 - 144x + 144
106. 49x^2 - 196x + 196
107. 64x^2 - 256x + 256
108. 81x^2 - 324x + 324
109. 100x^2 - 400x + 400
110. 121x^2 - 484x + 484
答案解析部分
1. x^2 - 4 = (x - 2)(x + 2)
2. x^2 - 9 = (x - 3)(x + 3)
3. x^2 - 16 = (x - 4)(x + 4)
4. x^2 - 25 = (x - 5)(x + 5)
5. x^2 - 36 = (x - 6)(x + 6)
6. x^2 - 49 = (x - 7)(x + 7)
7. x^2 - 64 = (x - 8)(x + 8)
8. x^2 - 81 = (x - 9)(x + 9)
9. x^2 - 100 = (x - 10)(x + 10)
10. x^2 - 121 = (x - 11)(x + 11)
...
（此处省略中间答案）
51. 2x^2 + 10x + 12 = 2(x^2 + 5x + 6) = 2(x + 2)(x + 3)
52. 3x^2 + 15x + 18 = 3(x^2 + 5x + 6) = 3(x + 2)(x + 3)
53. 4x^2 + 20x + 24 = 4(x^2 + 5x + 6) = 4(x + 2)(x + 3)
54. 5x^2 + 25x + 30 = 5(x^2 + 5x + 6) = 5(x + 2)(x + 3)
55. 6x^2 + 30x + 36 = 6(x^2 + 5x + 6) = 6(x + 2)(x + 3)
56. 7x^2 + 35x + 42 = 7(x^2 + 5x + 6) = 7(x + 2)(x + 3)
57. 8x^2 + 40x + 48 = 8(x^2 + 5x + 6) = 8(x + 2)(x + 3)
58. 9x^2 + 45x + 54 = 9(x^2 + 5x + 6) = 9(x + 2)(x + 3)
59. 10x^2 + 50x + 60 = 10(x^2 + 5x + 6) = 10(x + 2)(x + 3)
60. 11x^2 + 55x + 66 = 11(x^2 + 5x + 6) = 11(x + 2)(x + 3)
...
（此处省略中间答案）
101. 4x^2 - 16x + 16 = 4(x^2 - 4x + 4) = 4(x - 2)^2
102. 9x^2 - 36x + 36 = 9(x^2 - 4x + 4) = 9(x - 2)^2
103. 16x^2 - 64x + 64 = 16(x^2 - 4x + 4) = 16(x - 2)^2
104. 25x^2 - 100x + 100 = 25(x^2 - 4x + 4) = 25(x - 2)^2
105. 36x^2 - 144x + 144 = 36(x^2 - 4x + 4) = 36(x - 2)^2
106. 49x^2 - 196x + 196 = 49(x^2 - 4x + 4) = 49(x - 2)^2
107. 64x^2 - 256x + 256 = 64(x^2 - 4x + 4) = 64(x - 2)^2
108. 81x^2 - 324x + 324 = 81(x^2 - 4x + 4) = 81(x - 2)^2
109. 100x^2 - 400x + 400 = 100(x^2 - 4x + 4) = 100(x - 2)^2
110. 121x^2 - 484x + 484 = 121(x^2 - 4x + 4) = 121(x - 2)^2
通过以上练习和解答，希望大家能对因式分解有更深入的理解。因式分解虽然看似简单，但却是解决许多复杂问题的关键步骤。希望大家能够在日常学习中多加练习，不断提高自己的解题能力。
