(14) \( a^{3}+a^{2}+a+1= \)

To simplify the expression \( a^{3}+a^{2}+a+1 \), you can factor it. Notice that you can group it as follows: \[ a^3 + 1 + a^2 + a = (a^3 + 1) + (a^2 + a) \] Then, the term \( a^3 + 1 \) can be factored using the sum of cubes: \[ a^3 + 1 = (a + 1)(a^2 - a + 1) \] Thus, the entire expression becomes: \[ a^3 + a^2 + a + 1 = (a + 1)(a^2 - a + 1) + (a^2 + a) \] However, a more straightforward factorization can be found: \[ a^{3}+a^{2}+a+1 = (a^2 + 1)(a + 1) \] So the final factored form is: \[ a^{3}+a^{2}+a+1 = (a + 1)(a^2 + 1) \] This neat result shows how polynomial expressions can be pulled apart into simpler parts!