The document contains problems involving factorizing algebraic expressions in 6 activities. The problems involve factorizing expressions involving various combinations of variables, constants, and exponents. They require identifying common factors and grouping terms accordingly.

2. ACTIVIDAD
Nº 1

3. Problema 01:
Factoriza:
x6y3 – x4y5 + x2y7
2a4b – 4ab4 – 6a4b4
x2y – y – zy
7abc – 35abc2
15xyz3 – 5xy3z + 25x3yz
6a8 + 12a6 – 18a4 + 24a2

4. Problema 02:
Factoriza:
(x + 4)y – (x + 4)z
nx – 2ny – mx + 2my
x2 + xy + zx + zy
ax – bx + ay – by
 abc + ab + c + 1
x5 + ax3 + 2a2 + 2ax2

5. Problema 03:
Factoriza:
 x + y + 3xz + 3yz
 n + 2m2 + 1 + 2m2n
 3axy + 3axz + y + z
 ax + bx – cx + ay + by – cy
 w2x5 + 3w2 – t3x5 – 3t3
 5a2x + 3a2y – 5b3x – 3b3y

6. Problema 04:
Factoriza:
(m + n – 1)x2 + (m + n – 1)x – (m +
n – 1)
(a2 + b2)3a + (a2 + b2)5c + (a2 + b2)2
 (m2 + n)(x - y) – (m2 + n)(2x + 5y)
 (x + y)3 – (x + y)4z
 (x + y)(a + b) + (x + y)(m + n)

7. Problema 05:
Factoriza:
(a + b)m2 + (a + b)n
 (x + y)a3 + (x + y)b2
 (a + 2b)x4 + (2b + a)y3
 (m2 + n2)x2 + (m2 + n2)y2
 (a + b + 1)2 – (a + b + 1)(x – 2)
+ (a + b + 1)

8. Problema 06:
Factoriza:
ax + az + bx + bz
mx – m – x + 1
xy – zy + xt + zt
x5 + x3 + x2 + 1
ab + bc + xa + xc

9. ACTIVIDAD
Nº 2

10. Problema 01:
Factoriza:
x + y + 3xz + 3yz
n + 2m2 + 1 + 2m2n
3axy + 3axz + y + z
z + 3axy + y + 3axz
a2 – 3 + a2n – 3n

11. Problema 02:
Factoriza:
 ya + yb
 25x2 – 50x
 3m2 + 6m
 2ab – 2ay + 3bx – 3xy
 x9y4 – x4y6
 mx + xy –mz – yz
 x6 – 4x4 – x2

12. Problema 03:
Factoriza:
(x – 4)y – (x – 4)z
x(x + 7) + y(x + 7) – z(x + 7)
x4(2a + 5b) + x(2a + 5b) – (2a + 5b)
a(p – q) + b(p – q) + c(p – q)
mz + m2 + zy + my
az + bz + cz + ay + by + cy

13. Problema 04:
Factoriza:
 m3 – mn + mp – np
 m3 + m2 + m + 1
 m2 + mn + mp + np
 – m – n + x(m +n)
 x(3m – 2b) – 3m + 2b
 (c + 1)(b + 1) + (a + b)(c + 1)
 3b(2x + 3) + 2x + 3

14. Problema 05:
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

15. Problema 06:
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

16. ACTIVIDAD
Nº 3

17. Problema 01:
Factoriza:
(x – y)a + (x – y)b
(a + b)m2 + (a + b)n
(x + y)a3 + (x + y)b2
(a+ 2b)x4 + (2b + a)y3
(m2 + n2)x2 + (m2 + n2)y2

18. Problema 02:
Factoriza:
(a + b + c)x + (a + b + c)y
(m3 + n4)a4 – (m3 + n4)b3
(x + y)3 – (x + y)4z
(m2 + n) (x – y) – (m2 + n) (2x +
5y)
(x4 – a)3y2 – (x4 – a)(y – 1)

19. Problema 03:
Factoriza:
x2 + xy + zx + zy
ax – bx + ay – by
mnp + mn + c + 1
x5 + ax3 + 2a2 + 2ax2
x2y + xy + zx + z

20. Problema 04:
Factoriza:
 2a8b7 – 4a6b9 – 8a5b10
 15a4b5 + 30a8b7 – 10a6b4
 m4x – m5y + m3
 m7 + 2m10 – m8x
 xn + 5 + xn + 8 + xn + 4
 nx – 2ny – mx + 2my

21. Problema 05:
Factoriza:
2x3y + 3y2x
4a2b3 + 4a3b2 + 8ab
yx8 + yx6
x8y2 – 2x7y5
7x6y9 – 5x7y5