## Simplifying the Expression: (8b^3 - 6 + 3b^4) - (b^4 - 7b^3 - 3)

To simplify the expression **(8b^3 - 6 + 3b^4) - (b^4 - 7b^3 - 3)**, we need to follow the order of operations and combine like terms.

**1. Distribute the negative sign:**

Remember that subtracting a quantity is the same as adding the negative of that quantity. So, we distribute the negative sign to the terms inside the second set of parentheses:

**(8b^3 - 6 + 3b^4) + (-1 * b^4) + (-1 * -7b^3) + (-1 * -3)**

This simplifies to:

**(8b^3 - 6 + 3b^4) - b^4 + 7b^3 + 3**

**2. Combine like terms:**

We group the terms with the same variable and exponent together:

**(3b^4 - b^4) + (8b^3 + 7b^3) + (-6 + 3)**

**3. Simplify:**

Performing the indicated operations, we get:

**2b^4 + 15b^3 - 3**

**Therefore, the simplified form of the expression (8b^3 - 6 + 3b^4) - (b^4 - 7b^3 - 3) is 2b^4 + 15b^3 - 3.**