Simplify :
(v) $p + 2 (q - ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ r + p)$

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Solution

$p + 2 (q - ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ r + p) = p + 2 (q - r - p)$

on removing the bar bracket,

$= p + 2 q - 2 r - 2 p$

on removing small bracket,

$= p + 2 q - 2 r - 2 p$

$= - p + 2 q - 2 r$

Hence, $p + 2 (q - ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ r + p)$ = -p + 2q - 2r

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