(3a^4b+4ab^3)+(5ab^3-3a^4b

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3a^4b+4ab^3+5ab^3-3a^4b

Combine like terms.

3a^4b-3a^4b = 0

4ab^3+5ab^3 = ?

To simplify the expression (3a^4b + 4ab^3) + (5ab^3 - 3a^4b), you can collect like terms by combining the coefficients of the same variables.

First, let's add the terms that have the variable a^4b. The coefficients of these terms are 3 and -3, so they cancel each other out. Therefore, the a^4b term is eliminated from the expression.

Next, let's add the terms that have the variable ab^3. The coefficients of these terms are 4 and 5, so you can add them together to get 9. The variable ab^3 remains unchanged.

Therefore, the simplified expression is 9ab^3.

In summary:

(3a^4b + 4ab^3) + (5ab^3 - 3a^4b) = 9ab^3