Show that: $(9 p - 5 q)^{2} + 180 p q = (9 p + 5 q)^{2}$

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Solution

$(9 p - 5 q)^{2} + 180 p q = (9 p + 5 q)^{2}$

LHS $= (9 p)^{2} - 2 (9 p) (5 q) + (5 q)^{2} + 180 p q$
$= 81 p^{2} - 90 p q + 25 q^{2} + 180 p q$
$= 81 p^{2} + 90 p q + 25 q^{2}$

RHS $= (9 p + 5 q)^{2}$
$= (9 p)^{2} + 2 (9 p) (5 q) + (5 q)^{2}$
$= 81 p^{2} + 90 p q + 25 q^{2}$

LHS=RHS

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