Show that (4/3m - 3/4n) square +2mn = 16/9m square +9/16n square
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Answer:
L.H.S. = (4m/3 - 3n/4)² + 2mn
= {(4m/3)² - (2 × 4m/3 × 3n/4) + (3n/4)²} + 2mn,
using the identity
(a - b)² = a² - 2ab + b²
= 16m²/9 - 2mn + 9n²/16 + 2mn
= 16m²/9 + 9n²/16
= R.H.S.
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