Answer :
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.
### 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.
