Add or subtract the polynomials. 5. \( \left(-3 a^{3}+2 a^{2}-4\right)+\left(a^{3}-3 a^{2}-5 a+7\right) \) \( 6 .\left(7 x^{2} y^{2}-6 x^{3}+x y\right)-\left(5 x^{2} y^{2}-x^{3}+x y+x\right) \)

To add or subtract the polynomials, we combine like terms. For the first polynomial: \[ \left(-3 a^{3}+2 a^{2}-4\right)+\left(a^{3}-3 a^{2}-5 a+7\right) \] Combine the like terms: \[ -3 a^{3} + a^{3} + 2 a^{2} - 3 a^{2} - 5 a + (-4 + 7) = (-3 + 1)a^{3} + (2 - 3)a^{2} - 5a + 3 \] This simplifies to: \[ -2 a^{3} - a^{2} - 5 a + 3 \] For the second polynomial: \[ 6 \left( 7 x^{2} y^{2} - 6 x^{3} + x y \right) - \left( 5 x^{2} y^{2} - x^{3} + x y + x \right) \] Distributing the 6: \[ 42 x^{2} y^{2} - 36 x^{3} + 6 x y - (5 x^{2} y^{2} - x^{3} + x y + x) \] This becomes: \[ 42 x^{2} y^{2} - 36 x^{3} + 6 x y - 5 x^{2} y^{2} + x^{3} - x y - x \] Combining like terms: \[ (42 - 5)x^{2}y^{2} + (-36 + 1)x^{3} + (6 - 1)xy - x \] Which simplifies to: \[ 37 x^{2} y^{2} - 35 x^{3} + 5 x y - x \]