Finding the Product
To find the product of 1/4 * a^2 * b(5b^2 - 3ab), we will follow the steps of distribution and multiplication.
Step 1: Distribute the Terms
- Start with the expression: 1/4 * a^2 * b(5b^2 - 3ab).
- Apply the distributive property to multiply b with each term inside the parentheses.
Step 2: Expand the Expression
- Distributing b:
- b * 5b^2 = 5b^3
- b * (-3ab) = -3ab^2
Now, we can rewrite the expression as:
1/4 * a^2 * (5b^3 - 3ab^2).
Step 3: Multiply by 1/4 and a^2
- Now, multiply each term in the parentheses by 1/4 * a^2:
- 1/4 * a^2 * 5b^3 = (5/4)a^2b^3
- 1/4 * a^2 * (-3ab^2) = - (3/4)a^3b^2
Final Expression
Combining these results, we get the final product:
(5/4)a^2b^3 - (3/4)a^3b^2.
Conclusion
The product of the original expression is:
(5/4)a^2b^3 - (3/4)a^3b^2.
This expression is simplified and represents the final answer.