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