Simplify:
$(2 p + 3 q + 4 r) (9 p - r) + (p + q + r)$

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Solution

Given expression $(2 p + 3 q + 4 r) (9 p - r) + (p + q + r)$
$= (9 p) (2 p + 3 q + 4 r) + (- r) (2 p + 3 q + 4 r) + p + q + r$
$= 18 p^{2} + 27 p q + 36 p r - 2 p r - 3 q r - 4 r^{2} + p + q + r$
$= 18 p^{2} + 27 p q + 34 p r - 3 q r - 4 r^{2} + p + q + r$
Hence, $(2 p + 3 q + 4 r) (9 p - r) + (p + q + r) = 18 p^{2} + 27 p q + 34 p r - 3 q r - 4 r^{2} + p + q + r$

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