The document contains a series of math problems asking to factorize various expressions. The expressions include variables, numbers, and operations like addition, subtraction, multiplication and exponents. They range in complexity from single term expressions to multi-term expressions involving multiple variables. The goal of the problems is to practice factorizing algebraic expressions.

2. ACTIVIDAD Nº 1

3. Factoriza:
 xa + xb
 25x2 – 49
 m2 + 6m + 9
 ab – ay + bx – xy
 x7y4 – x5y6
 mx2 + xy – xz – yz
 x5 – 4x3 – x2 + 4

4. Factoriza:
 (x – 2)y – (x – 2)z
 x(x + 5) + y(x + 5) – z(x + 5)
 x4(2a – 5b) + x(2a – 5b) – (2a – 5b)
 a(p + q) + b(p + q) + c(p + q)
 mx + m2 + xy + my
 ax + x2 + ab + bx
 ax + bx + cx + ay + by + cy

5. Factoriza:
 m2 – mn + mp – np
 m3 + m2 + m + 1
 m2 + mn + mp + np
 – m – n + x(m +n)
 x(3a – 2b) – 3a + 2b
 (c + 1)(ab + 1) + (a + b)(c + 1)
 3b(2x + 3) + 2x + 3

6. Factoriza:
 x2 + y2 – 5y(x2 + y2)
 1 – x – 2y(1 – x)
 x3 – x2 + x – 1
 5y5 – 15y2z + y3 – 3z
 a5 – a4 + a – 1
 3xy – 3xz + 3x – y + z – 1
 2a2x + 2ax + 2x – a2 – a – 1

7. Factoriza:
 x2y2 + x2y + xy2 + xy
 x3y2 + x2y + x2y3 + xy2
 x4y – x2y3 – x3y2 + xy4
 x3 + 2x2y + 4xy2 + 8y3
 a2 – abc – ac – ab + b2c + bc
 (x2 + 2)2 – (2x - 1)2
 (x2 – y2)2 – (y2 – z2)2

8. ACTIVIDAD Nº 2

9. Factoriza:
 x3 + x2 – 9x – 9
 (x + 1)4 – 5(x + 1)2 + 4
 (x2 + 5)2 + 13x(x2 + 5) + 42x2
 x5y4 + x5y2 + x3y4 + x3y2
 (x – 3)(x – 2)(x – 1) + (x – 1)(x – 2) –
(x – 1)
 x2 – (ac – b)x – abc

10. Factoriza:
 a(x – 1) – b(1 – x) + cx – c
 8x2 + 9ac – 6ax – 12cx
 a3 – ab2 + a2b – b3 + a2 – b2
 16x2n + 1 + 12x3n – 20xn–1
 (x + 3)(x + 2)(x + 1) + (x + 2)(x + 1) +
(x + 1)
 (x + 2)(x + 3)(x + 4) + (x + 3)(x + 4) –
(x + 4)

11. Factoriza:
8x2 – 22x + 15
7x2 + 29x – 36
25x4 – 109x2 + 36
4x4 – 37x2 + 9
6x4y3 – x3y4 – 15x2y5
16m8 – 17m4n4 + n8

12. Factoriza:
8x6 + 215x3 – 27
(x2 – 5x + 3)2 + 4x2 – 20x + 15
(x–3)2 – 2(x–3)(y–2) – 3(y–2)2
22m+5 – 3.2m+2 – 35
32m+2 – 3m+1 – 30
x2m+4 – 5xm+4 – 50x4

13. Factoriza:
 x5 + x3 - 2x2 - 2
 x2yz + x2yc + xy2z + cxy2
 x4 - 5x2y2 + 4y4
 x4y3 - 2x3y4 + x2y5
 8x2 - 22x + 15
 x4 - 6x2 - 27
 x2 + 5xy + 6y2 + x + 5y – 6

14. ACTIVIDAD Nº 3

15. Factoriza:
3(x – a)2 – 4(x – a) + 1
5a9b3 + 15a6b7
a3 + a2b + ab2 + b3
8x3 + 27
(x + 1)4 – (x – 1)4
x5 + x2 – x – 1

16. Factoriza:
 a(1 – b2) + b(1 – a2)
 a(b2 + c2) + b(c2 + a2)
 wy + wz – wyz – xy – xz + xyz
 49x2 – 14x + 1
 x2 – 6x – 7
 x2 – 21x + 20
 x2 + 8x + 15

17. Factoriza:
12x3y2z3 – 15x2yz3 – 6x2y3z4 +
9x3y5z3
7x2a – 14xa + 3 + 7xa
3m(a – b + c) – 2n(b – a – c)
2x2 + 2cx – 3bx – 3bc
x3 + x2 + x + 1

18. Factoriza:
a3b4c2 + a2b5c2 + a3b3c3 +
a2b4c3
64x12y3 – 68x8y7 + 4x4y11
x5 – 2x4 –x + 2
x3y – 2x2y + 3xy2
x2yz + 2xy2z + 3xyz2
6 5 4 3

19. Factoriza:
 x2 – 81
 25 – m2
 9x2 – 1
 16 – 9a2
 (x - 1)2 – 49
 (a – b)2 – 4
 16x2 – 81y2