Simply expand it and compute the discriminant

Algebra Level 2

$\large{\color{#624F41}{(\color{#3D99F6}{b}\color{#20A900}{+c}\color{#D61F06}{-a})(\color{#D61F06}{a}\color{#3D99F6}{+b}\color{#20A900}{-c})(\color{#D61F06}{a}\color{#3D99F6}{-b}\color{#20A900}{+c})(\color{#D61F06}{a}\color{#3D99F6}{+b}\color{#20A900}{+c})\\ \times (\color{#D61F06}{a}\color{#3D99F6}{-b}\color{#20A900}{-c})(\color{#3D99F6}{b}\color{#D61F06}{-a}\color{#20A900}{-c})(\color{#20A900}{c}\color{#D61F06}{-a}\color{#3D99F6}{-b})(\color{#D61F06}{-a}\color{#3D99F6}{-b}\color{#20A900}{-c})}}$

Suppose $a,b,c$ are integers, is the above product a square?