1. **State the problem:** Simplify and understand the function $f(x) = (x \cdot x^2 + 3x - 1)^3$. 2. **Rewrite the expression inside the parentheses:** Note that $x \cdot x^2 = x^{1+2} = x^3$. So the expression becomes: $$ (x^3 + 3x - 1)^3 $$ 3. **Explain the formula:** The function is a cube of a polynomial. The cube of a sum $(a + b + c)^3$ can be expanded using the binomial or multinomial theorem, but here we will keep it in the compact form unless expansion is requested. 4. **Intermediate work:** The simplified inner expression is $x^3 + 3x - 1$. The function is: $$ f(x) = (x^3 + 3x - 1)^3 $$ 5. **Learner-friendly explanation:** We first combined the powers of $x$ by adding exponents when multiplying like bases. Then we recognized the entire expression is raised to the third power, which means the whole polynomial is multiplied by itself three times. 6. **Final answer:** $$ f(x) = (x^3 + 3x - 1)^3 $$