Simplify $(p - 2 q + r)^{2} - (- p + 2 q - r)^{2}$

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Solution

$(p - 2 q + r)^{2} - (- p + 2 q - r)^{2}$
Using $a^{2} - b^{2} = (a + b) (a - b)$
$= (p - 2 q + r - p + 2 q - r) [p - 2 q + r - (- p + 2 q - r)]$
$= 0$

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