Question

show that (4/3m-3/4n)^2+2mn=16/9m^2 square +9/16n^3

Answer 1

$\bold{Answer :}$

Now,

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.

Hence, proved.

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