Alright, let's solve the algebraic operations as outlined in the question.
### Monomio por término independiente
1. \(4(v)\):
[tex]\[
4v
\][/tex]
2. \((ab) \cdot 2\):
[tex]\[
2ab
\][/tex]
3. \(\exists(z\cdot b)\):
[tex]\[
zb
\][/tex]
4. \(12(y^2)\):
[tex]\[
12y^2
\][/tex]
5. \((x^2) \cdot 15\):
[tex]\[
15x^2
\][/tex]
6. \((ab) \cdot \frac{1}{8}\):
[tex]\[
\frac{1}{8}ab
\][/tex]
### Monomio por monomio
1. \(a \cdot (2a)\):
[tex]\[
2a^2
\][/tex]
2. \(x \cdot (10x)\):
[tex]\[
10x^2
\][/tex]
3. \(2a \cdot (4a)\):
[tex]\[
8a^2
\][/tex]
4. \(y \cdot (0y)\):
[tex]\[
0
\][/tex]
5. \(a \cdot (5b)\):
[tex]\[
5ab
\][/tex]
6. \(ab \cdot (2b)\):
[tex]\[
2ab^2
\][/tex]
7. \(ab \cdot (sac)\):
[tex]\[
absac
\][/tex]
8. \(3x \cdot (xy)\):
[tex]\[
3x^2y
\][/tex]
9. \text{Sa} \cdot (4ab):
[tex]\[
4 \text{Sa}ab
\][/tex]
10. \((8b) \cdot 9\):
[tex]\[
72b
\][/tex]
11. \(4(2x)\):
[tex]\[
8x
\][/tex]
12. \(-3(3x)\):
[tex]\[
-9x
\][/tex]
13. \(ab(2b)\):
[tex]\[
2ab^2
\][/tex]
### Monomio por binomio
1. \(x(5x + 4)\):
[tex]\[
x(5x) + x(4) = 5x^2 + 4x
\][/tex]
2. \(2x(3x - 3x)\):
[tex]\[
2x(3x) - 2x(3x) = 6x^2 - 6x^2 = 0
\][/tex]
3. \((5b + b)7b\):
[tex]\[
(6b)7b = 42b^2
\][/tex]
4. \(ab(a + 2b)\):
[tex]\[
ab(a) + ab(2b) = a^2b + 2ab^2
\][/tex]
5. \(3z(2x + 3)\):
[tex]\[
3z(2x) + 3z(3) = 6zx + 9z
\][/tex]
6. \((3b - 2a)5ab\):
[tex]\[
(3b)5ab - (2a)5ab = 15ab^2 - 10a^2b
\][/tex]
7. \((5b + 2)7b\):
[tex]\[
(5b)7b + (2)7b = 35b^2 + 14b
\][/tex]
8. \(x(ax + 9y)\):
[tex]\[
x(a x) + x(9y) = a x^2 + 9xy
\][/tex]
9. \(a(3a + 4)\):
[tex]\[
a(3a) + a(4) = 3a^2 + 4a
\][/tex]
This detailed solution covers all the algebraic operations requested, step by step.
