1. The problem is to simplify or understand the expression $a^2 + b^2$. 2. This expression represents the sum of the squares of two variables $a$ and $b$. 3. There is no further simplification possible for $a^2 + b^2$ unless additional information or values for $a$ and $b$ are given. 4. This expression is commonly seen in algebra and geometry, for example in the Pythagorean theorem where $a^2 + b^2 = c^2$ for a right triangle. 5. Without more context, the expression remains as $a^2 + b^2$. Final answer: $a^2 + b^2$