Exciting Math Problem to Solve!

To solve this math problem, we need to combine like terms and simplify the expression step by step. Let's break it down:

Step 1: Combine like terms

First, let's add the terms in the parentheses together:

(-4b^2 + 8b) + (-4b^3 + 5b^2 - 8b)

Combine the terms with the same variables:

-4b^2 + 8b - 4b^3 + 5b^2 - 8b

Step 2: Simplify the expression

Combine the like terms:

-4b^2 + 8b - 4b^3 + 5b^2 - 8b

Combine the terms with the same variables:

(-4b^3) + (5b^2 - 4b^2 - 8b + 8b)

-4b^3 + b^2

Step 3: Final Answer

After combining like terms and simplifying the expression, the final result is:

-4b^3 + b^2

So, the answer to the math problem (-4b^2 + 8b) + (-4b^3 + 5b^2 - 8b) is -4b^3 + b^2. Congrats on solving the problem! Keep up the great work in math!