Expansions-12

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(i) (2x + 3y + 5) (2x + 3y + 2)

(ii) (3x - y + 4) (3x - y - 7)

Solution :

(i) (2x + 3y + 5) (2x + 3y + 2)

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

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

= a 2 + (5 + 2) a + 5 X 2 [(x + a) (x + b) = x 2 + (a + b) x + ab ]

= a 2 + 7a + 10

= (2x + 3y) 2 + 7 (2x + 3y) + 10

= ( 2x ) 2 + 2 X 2x X 3y + ( 3y ) 2 + 14x + 21y + 10

= 4x 2 + 12 xy + 9 y 2 + 14 x + 21y + 10

(ii) (3x - y + 4) (3x - y - 7)

= [ (3x - y) + 4] [ (3x - y) - 7]

= (a + 4) (a - 7) [Taking 3x - y = a]

= a 2 + (4 - 7) a + 4 ( - 7) [ (x + a) (x + b) = x 2 + (a + b) x + ab ]

= a 2 - 3a - 28

= (3x - y) 2 - 3 (3x - y) - 28

= (3x) 2 - 2 X 3x X y + y 2 - 9x + 3y - 28

= 9 x 2 - 6 x y + y 2 - 9 x + 3 y - 28

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