The expression you provided is:

$a + \frac{a^3}{4}$

This expression cannot be simplified further through standard algebraic manipulation because it involves the sum of two terms that do not share a common factor.

Interpretation:

1. The first term is simply $a$.
2. The second term is $\frac{a^3}{4}$, which means $a^3$ divided by 4.

Final Expression:

So, the expression remains as:

$a + \frac{a^3}{4}$

This is the simplest form unless you intend to factorize or expand further, depending on the context.

Would you like more details or have any questions?

Here are some related questions:

1. How can you factor expressions involving sums like $a + \frac{a^3}{4}$?
2. What is the process of adding algebraic fractions?
3. How can such expressions be used in polynomial equations?
4. What are some common algebraic techniques for simplifying sums?
5. How do you apply operations to polynomials?

Tip: When adding terms in algebra, always check if there’s a common factor that can simplify the expression further. If not, the expression may already be in its simplest form.