Factors-7

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Factorize :

(i) x 2 - 25

(ii) 9 (x - y) 2 - (x + 2 y) 2

(iii) 48 x 3 - 27 x

(iv) 16 a 4 - b 4

Solution:

(i) x 2 - 25 = x 2 - 5 2 = (x + 5) (x - 5)

(ii) 9 (x - y) 2 - (x + 2 y) 2 = [(3x - 3y) 2 - (x + 2 y) 2 ]

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

= (4 x - y) (2 x - 5 y)

(iii) 48 x 3 - 27 x = 3 x (16 x 2 - 9)

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

= 3 x (4 x + 3) (4 x - 3)

(iv) 16 a 4 - b 4

= (4 a 2 ) 2 - (b 2 ) 2

= (4 a 2 + b 2 ) (4 a 2 - b 2 )

= ( 4 a 2 + b 2 ) ( 2a + b ) ( 2a - b )

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