Question

Factorize a(b-c)^3 +b(c-a)^3+c(a-b)^3

Answer 1

Let's simplify step-by-step.

a(b−c)3+b(c−a)3+c(a−b)3

Distribute:

=ab3+−3ab2c+3abc2+−ac3+−a3b+3a2bc+−3abc2+bc3+a3c+−3a2bc+3ab2c+−b3c

Combine Like Terms:

=ab3+−3ab2c+3abc2+−ac3+−a3b+3a2bc+−3abc2+bc3+a3c+−3a2bc+3ab2c+−b3c

=(−a3b)+(a3c)+(3a2bc+−3a2bc)+(ab3)+(3ab2c+−3ab2c)+(−3abc2+3abc2)+(−ac3)+(−b3c)+(bc3)

=−a3b+a3c+ab3+−ac3+−b3c+bc3

Answer:

=−a3b+a3c+ab3−ac3−b3c+bc3