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ICSE Class 9 Answered

Factorise:- (a-b)^5 + (b-c)^5 + (c-a)^5
Asked by Amit | 21 Sep, 2018, 12:57: PM
answered-by-expert Expert Answer

Lets make the substitutions  p=b−a  and  q=c−b  so that  p+q=c−a 

The expression becomes

(a−b)5+(b−c)5+(c−a)5

= −p5−q5+(p+q)5

= 5p4q+10p3q2+10p2q3+5pq4

= 5pq(p3+2p2q+2pq2+q3)

= 5pq(p+q)(p2+pq+q2)

Resub

= 5(b−a)(c−b)(c−a)((p+q)2−pq)

= 5(a−b)(b−c)(c−a)((c−a)2−bc−ab+ac+b2)

= 5(a−b)(b−c)(c−a)(a2+b2+c2−ab−bc−ca)

Answered by Arun | 26 Sep, 2018, 10:42: AM

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