Factors-11

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Factorize :

(i) a 3 + 27 b 3

(ii) 16 a 4 + 54 a

(iii) 125 a 3 + 1 / 8

(iv) a 3 + b 3 + a + b

Solution :

(i) (i) a 3 + 27 b 3

= ( a ) 3 + ( 3 b ) 3

= (a + 3 b) [ ( a ) 2 - a X 3 b + ( 3 b ) 2 ]

= (a + 3 b) (a 2 - 3 a b + 9 b 2 )

(ii) 16 a 4 + 54 a

= 2 a ( 8 a 3 + 27)

= 2 a [(2 a) 3 + ( 3 ) 3 ]

= 2 a (2 a + 3) (4 a 2 - 6 a + 9)

(iii) 125 a 3 + 1 / 8

= ( 5 a ) 3 + ( 1 / 2 ) 3

= (5 a + 1 / 2) [ ( 5 a ) 2 - 5 a X 1 / 2 + ( 1 / 2 ) 2 ]

= (5 a + 1 / 2) (25 a 2 - 5 a / 2 + 1 / 4 )

(iv) a 3 + b 3 + a + b

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

= (a + b) (a 2 - a b + b 2 + 1)

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