1. The problem is to understand the expression $X^2 + b^2$ and explore its components. 2. This expression is a sum of squares, where $X$ and $b$ are variables or constants. 3. $X^2$ means $X$ multiplied by itself and $b^2$ means $b$ multiplied by itself. 4. This form is often used in algebra to represent the sum of squares, which cannot be simplified further without additional context or values. 5. If you want to evaluate or factor it, you need specific values or additional expressions. 6. For example, there is no direct factorization for $X^2 + b^2$ over the real numbers, but in complex numbers, it can be factored as $(X + bi)(X - bi)$. 7. Summary: The expression $X^2 + b^2$ is already in simplest form unless factoring over complex numbers is desired.