(9) \( \quad\left(1-a^{4}\right)\left(1-a^{2}\right)\left(1+a^{2}\right) \)

To simplify the expression: \[ \left(1 - a^{4}\right)\left(1 - a^{2}\right)\left(1 + a^{2}\right) \] we can follow these steps: 1. **Factor \(1 - a^{4}\):** Notice that \(1 - a^{4}\) is a difference of squares: \[ 1 - a^{4} = (1 - a^{2})(1 + a^{2}) \] 2. **Substitute the factorization back into the original expression:** \[ \left(1 - a^{4}\right)\left(1 - a^{2}\right)\left(1 + a^{2}\right) = \left[(1 - a^{2})(1 + a^{2})\right]\left(1 - a^{2}\right)\left(1 + a^{2}\right) \] 3. **Rearrange and combine like terms:** \[ (1 - a^{2}) \times (1 - a^{2}) \times (1 + a^{2}) \times (1 + a^{2}) = (1 - a^{2})^{2} \times (1 + a^{2})^{2} \] 4. **Final Factored Form:** \[ (1 - a^{2})^{2}(1 + a^{2})^{2} \] Alternatively, this can be fully factored further over the real numbers: \[ (1 - a)^2(1 + a)^2(1 + a^{2})^2 \] **Summary:** \[ \left(1 - a^{4}\right)\left(1 - a^{2}\right)\left(1 + a^{2}\right) = (1 - a^{2})^{2}\,(1 + a^{2})^{2} \] Or, more completely factored: \[ (1 - a)^2\, (1 + a)^2\, (1 + a^{2})^2 \]