Subjects algebra

Quadratic Expression 01E1E0

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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.