Expansions-8

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Evaluate : (i) (2 a + 3 b) 3 (ii) (4 a - 5 b) 3 (iii) (2 x - 3 y + 5) 3

Solution :

(i) (2 a + 3 b) 3 = (2 a) 3 + 3 (2 a) 2 (3 b) + 3 (2 a) (3 b) 2 + (3 b) 3

= 8 a 3 + 36 a 2 b + 54 a b 2 + 27 b 3

(ii) (4 a - 5 b) 3 = (4 a) 3 - 3 (4 a) 2 (5 b) + 3 (4 a) (5 b) 2 - (5 b) 3

= 64 a 3 - 240 a 2 b + 300 a b 2 - 125 b 3

(iii) (2 x - 3 y + 5) 3 = (a + 5) 3 [Taking 2 x - 3 y = a]

= a 3 + 5 3 + 3 a X 5 (a + 5)

= (2 x - 3 y) 3 + 125 + 15 (2 x - 3 y) (2 x - 3 y + 5)

= (2 x) 3 - (3 y) 3 - 3 X 2 x X 3 y (2 x - 3 y) + 125 + 60 x 2 - 90 x y + 150 x - 90 x y + 150 x - 90 x y + 135 y 2 - 225 y

= 8 x 3 - 27 y 3 - 36 x 2 y + 54 x y 2 + 125 + 60 x 2 + 135 y 2 - 180 x y + 150 x - 225 y

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