Question
Fri September 07, 2012 By: Pranav Gupta

Factorise p3-125q3 +1+15pq

Expert Reply
Sat September 08, 2012

p3 - 125q3 + 1 + 15pq

= (p)3 + (-5q)3 + 13 -3 × p × (-5q) × 1

=  [p + (-5q) + 1] [p2 + (-5q)2 + 12 - p × (-5q) - (-5q) × 1 - 1 × p]

[It is because of a3 + b3 + c3 -3abc = (a + b + c) (a2 + b2 + c2 - ab - bc - ca)]

=  (p -5q + 1) (p2 + 25q2 + 1 + 5pq + 5q - p)

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