`a,`
`a(b^2-c^2)+b(c^2-a^2)+c(a^2-b^2)`
`= a(b-c)(b+c)+bc^2-a^2b+a^2c-b^2c`
`= a(b-c)(b+c)-(b^2c-bc^2)-(a^2b-a^2c)`
`= a(b-c)(b+c)-bc(b-c)-a^2(b-c)`
`= (b-c)[a(b+c)-bc-a^2]`
`= (b-c)(ab+ac-bc-a^2)`
`= (b-c)[(ab-bc)+(ac-a^2)]`
`= (b-c)[b(a-c)+a(c-a)]`
`= (b-c)[b(a-c)-a(a-c)]`
`= (b-c)(b-a)(a-c)`
$\text {@lamtung2007}$