Simply expand it and compute the discriminant

Algebra Level 2

\[\large{\color{brown}{(\color{blue}{b}\color{green}{+c}\color{red}{-a})(\color{red}{a}\color{blue}{+b}\color{green}{-c})(\color{red}{a}\color{blue}{-b}\color{green}{+c})(\color{red}{a}\color{blue}{+b}\color{green}{+c})\\ \times (\color{red}{a}\color{blue}{-b}\color{green}{-c})(\color{blue}{b}\color{red}{-a}\color{green}{-c})(\color{green}{c}\color{red}{-a}\color{blue}{-b})(\color{red}{-a}\color{blue}{-b}\color{green}{-c})}}\]

Suppose \(a,b,c\) are integers, is the above product a square?

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