30) \( \left(y^{3}-7 x^{4} y^{4}\right)+\left(-10 x^{4} y^{3}+6 y^{3}+4 x^{4} y^{4}\right)-\left(x^{4} y^{3}+6 x^{4} y^{4}\right) \)

To simplify the expression, let’s first combine like terms step by step: 1. Start by writing the expression: \[ (y^{3} - 7x^{4}y^{4}) + (-10x^{4}y^{3} + 6y^{3} + 4x^{4}y^{4}) - (x^{4}y^{3} + 6x^{4}y^{4}). \] 2. Distribute the negative sign in the last term: \[ = y^{3} - 7x^{4}y^{4} - 10x^{4}y^{3} + 6y^{3} + 4x^{4}y^{4} - x^{4}y^{3} - 6x^{4}y^{4}. \] 3. Now, combine like terms. Group \(y^{3}\) terms and \(x^{4}y^{4}\) terms together: - For \(y^{3}\): \[ y^{3} + 6y^{3} - 10x^{4}y^{3} - x^{4}y^{3} = (1 + 6 - 10 - 1)x^{4}y^{3} = (-4)x^{4}y^{3}. \] - For \(x^{4}y^{4}\): \[ -7x^{4}y^{4} + 4x^{4}y^{4} - 6x^{4}y^{4} = (-7 + 4 - 6)x^{4}y^{4} = (-9)x^{4}y^{4}. \] 4. Combine everything to get the final simplified expression: \[ -4x^{4}y^{3} - 9x^{4}y^{4}. \] Thus, the simplified expression is: \[ -4x^{4}y^{3} - 9x^{4}y^{4}. \]