Factors-14

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Factorize :

(i) a2 + 1 / a2 - 18

(ii) a4 - 7a2 + 1

(iii) a3 + 3a2b + 3ab2 + 2b3

Solution :

(i) a2 + 1 / a2 - 18

= ( a2 + 1 / a2 - 2 ) - 16

= (a - 1 / a)2 - (4)2

= (a - 1 / a + 4) (a - 1 / a - 4)

(ii) a4 - 7a2 + 1

= (a4 + 1 + 2a2) - 9a2

= (a2 + 1) 2 - (3a)2

= (a2 + 3a + 1) (a2 - 3a + 1)

(iii) a 3 + 3 a2b + 3 ab2 + 2b3

= a3 + 3a2b + 3ab2 + b3 + b3

= (a + b)3 + b3

= x3 + b3 …[Taking a + b = x]

= (x + b) (x2 - bx + b2)

= (a + b + b) [(a + b)2 - b (a + b) + b2]

= (a + 2b) (a2 + 2 ab + b2 - ab - b2 + b2)

= (a + 2b) (a2 + ab + b2)

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