Expansions-2

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Evaluate :

(i) [ (3x / 4) - (2y / 3) ] 2

(ii) [ (2x / 3) - (3y / 4) + (4z / 5)] 2

Solution:

(i) (a - b) 2 = a 2 - 2 a b + b 2

=> [ (3x / 4) - (2y / 3) ] 2 = (3x / 4) 2 - 2 X (3x / 4) X (2y / 3) + (2y / 3) 2

= (9 / 16) x 2 - x y + (4 / 9) y 2

(ii) (a + b + c) 2 = a 2 + b 2 + c 2 + 2 a b + 2 b c + 2 c a

=> [ (2x / 3) - (3y / 4) + (4z / 5)] 2 = (2x / 3) 2 + ( - 3y / 4) 2 + (4x / 5) 2 + 2 X (2x / 3) X (- 3y / 4) + 2 X ( - 3y / 4) X (4z / 5) + 2 X (4z / 5) X (2x / 3)

= (4 / 9) x 2 + (9 / 16) y 2 + (16 / 25) z 2 - xy - (6 yz / 5) + (16 / 15) zx

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