Sure! Let's tackle this question step by step.
### Monomial by Constant Term
We will multiply each monomial by the given constant term:
1. \( 4(y) = 4y \)
2. (ab) \( 2 = (ab) \cdot 2 = 2ab \)
3. \( 3(3 b') = 3 \cdot 3b' = 9b' \)
4. \( 12(y^2) = 12y^2 \)
5. \( (x^2 y) \cdot 5 = x^2 y \cdot 5 = 5x^2 y \)
6. (ab) \( \frac{1}{8} = ab \cdot \frac{1}{8} = \frac{ab}{8} \)
### Monomial by Monomial
Now, we multiply each pair of monomials:
1. \( 2a = 2a \)
2. \( x(10x) = x \cdot 10x = 10x^2 \)
3. \( 2a(4a) = 2a \cdot 4a = 8a^2 \)
4. \( y(8y) = y \cdot 8y = 8y^2 \)
5. \( a(8b) = a \cdot 8b = 8ab \)
6. \( ab(2b) = ab \cdot 2b = 2ab^2 \)
7. \( 4b(8bc) = 4b \cdot 8bc = 32b^2c \)
8. \( 3x(x y) = 3x \cdot xy = 3x^2y \)
9. \( 9a(4ab) = 9a \cdot 4ab = 36a^2b \)
10. \( (8b) \cdot 9 = 8b \cdot 9 = 72b \)
11. \( 4(2x) = 4 \cdot 2x = 8x \)
12. \( -3(8x) = -3 \cdot 8x = -24x \)
### Monomial by Binomial
Finally, we will distribute each monomial across the terms of the binomial:
1. \( x(5x - 4) = x \cdot 5x - x \cdot 4 = 5x^2 - 4x \)
2. \( 2x(8x - 3x) = 2x \cdot 8x - 2x \cdot 3x = 16x^2 - 6x^2 = 10x^2 \)
3. \( (6b \div b) \cdot 7b = 6 \cdot 7b = 42b \)
4. \( 4b(a - 2b) = 4b \cdot a - 4b \cdot 2b = 4ab - 8b^2 \)
5. \( 62 \left( \frac{2x}{3} \right) = 62 \cdot \frac{2x}{3} = \frac{124x}{3} \)
6. \( (3b - 2a) \cdot 5ab = 3b \cdot 5ab - 2a \cdot 5ab = 15ab^2 - 10a^2b \)
7. \( (5b + 2) \cdot 7b = 5b \cdot 7b + 2 \cdot 7b = 35b^2 + 14b \)
8. \( x \left( \frac{8x}{9y} \right) = x \cdot \frac{8x}{9y} = \frac{8x^2}{9y} \)
9. \( a(3a + 4) = a \cdot 3a + a \cdot 4 = 3a^2 + 4a \)
This completes the detailed step-by-step solution for the given problem.
