Quadratic Expression 01E1E0
1. The problem is to simplify or understand the expression $a^2 + b^2 - ab$.
2. This expression is a quadratic form in terms of $a$ and $b$.
3. There is no direct factorization into simple binomials, but it can be rewritten using the identity:
$$a^2 + b^2 - ab = \frac{1}{2} \left(2a^2 + 2b^2 - 2ab\right) = \frac{1}{2} \left((a-b)^2 + a^2 + b^2\right)$$
4. Alternatively, it can be left as is or used in problems involving sums of squares and products.
5. This expression is always non-negative for real numbers $a$ and $b$ because it can be related to sums of squares.
Final answer: The expression $a^2 + b^2 - ab$ is simplified as is or can be expressed as $$a^2 + b^2 - ab$$ without further factorization.