Expansions-11

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(i) ( 3x - 2 y + 4 ) (3 x - 2 y - 4)

(ii) ( 5 x - 3 y + 2 ) (5 x + 3 y + 2)

Solution :

(i) ( 3x - 2 y + 4 ) (3 x - 2 y - 4)

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

(a + 4) (a - 4) [Taking 3x - 2y = a]

= (a 2 - 16)

= (3x - 2y) 2 - 16

= ( 3x ) 2 - 2 X 3x X 2y + ( 2y ) 2 - 16

= 9 x 2 - 12 x y + 4 y 2 - 16

(ii) ( 5 x - 3 y + 2 ) (5 x + 3 y + 2)

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

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

= a 2 - ( - 3y) 2

= (5x + 2) 2 - 9 y 2 = 25 x 2 + 20 x + 4 - 9 y 2

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