Q. 15

Factorise the following
(i) 16p3q3 + 54r3
(ii) + 8b3
(iii) 2 a3 + 3 b3
(iv) 8a4b + ab4
(v) a7 - 64a

Answer :

(i) 16p3q3 + 54r3
   = 2(8p3q3 + 27r3)
   = 2[(2pq)3 + (3r)3]
   = 2(2pq + 3r) [(2pq)2 - 2pq . 3r + (3r)2]
   = 2 (2pq + 3r) (4p2q2 - 6pqr + 9r2)
(ii) + 8b3 = ()3 + (2b)3
                = ( +2b)( -ab+4b2)
(iii) 2 a3 + 3 b3
    = ( a)3+( b)3
    = ( a + b)(2a2 - ab + 3b2)
(iv) 8a4b + ab4 = ab(8a3+ )
                          = ab[ ]
                          = ab (2a+ )
(v)  a7 - 64a
     = a(a6 - 64)
     = a(a6 - 26)
     = a[(a3)2 - (23)2]
     = a(a3 + 23) (a3 - 23)
     = a(a + 2) (a2 - 2a + 4) (a - 2) (a2 + 2a + 4)
     = a(a + 2) (a - 2) (a2 - 2a + 4) (a2 + 2a + 4)

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