(4/3m - 3/4n)2 + 2mn = 16/9 m2 + 9/16 n2

Answer:

(4/3m – 3/4n)2 + 2mn = 16/9 m2 + 9/16 n2

LHS = (4/3m – 3/4n)2 + 2mn

RHS = 16/9 m2 + 9/16 n2

Consider (4/3m – 3/4n)2

Using the identity

(a – b) 2 = a2 + b2 – 2ab

(4/3m – 3/4n)2 = (4/3m)2 + (3/4n)2 – 2 × (4/3m) × (3/4n)

(4/3m – 3/4n)2 = 16/9 m2 + 9/16 n2 – 2mn

LHS = (4/3m – 3/4n)2 + 2mn

LHS = 16/9 m2 + 9/16 n2 – 2mn + 2mn

LHS = 16/9 m2 + 9/16 n2

Thus LHS = RHS

Hence proved.

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