Question

Prove that |(a,b,c),(a²,b²,c²),(a³,b³,c³)| = abc(a - b)(b - c)(c - a)

Answer 1

(taking common from a, b, c respectively from, c₁,c₂,c₃)

(taking common (a - b))

from c₁, and (b - c) from c₂

= (abc)(a - b) (b - c) {(b + c) - (a + b)} 

= abc(a - b) (b - c) (c - a)

= R.H.S.