Final answer:
To simpliify the expression (6-z+z^(3))-(-3+4z^(2)-z^(3)), we first distribute the negative sign, then combine like terms to get the simplified expression 9-z+2z^(3).
Step-by-step explanation:
To simplify the expression (6-z+z^(3))-(-3+4z^(2)-z^(3)), we first distribute the negative sign to the terms inside the second set of parentheses. This gives us 6-z+z^(3)+3-4z^(2)+z^(3).
Next, we can combine like terms, which means adding or subtracting the coefficients of the same variables. In this case, the terms with z and z^(3) can be combined: -z+z^(3)+z^(3) = -z+2z^(3).
Finally, we simplify further by combining the constants: 6+3 = 9. Therefore, the simplified expression is 9-z+2z^(3).