Simplify $(3 p + 5 q - 2 r)^{2}$

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Solution

Formula to be used:
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
$(3 p + 5 q - 2 r)^{2}$
$= (3 p)^{2} + (5 q)^{2} + (- 2 r)^{2} + 2 (3 p) (5 q) + 2 (5 q) (- 2 r) + 2 (- 2 r) (3 p)$
$= 9 p^{2} + 25 q^{2} + 4 r^{2} + 30 p q - 20 q r - 12 r p$

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