Step-by-step explanation:
[tex]a(b+c-bc)-b(c+a-ac)+c(b-a)[/tex]
Distribute over the parenthesis:
[tex](ab+ac-abc)+(-bc-ab+abc)+(bc-ac)\\ab+ac-abc-bc-ab+abc+bc-ac[/tex]
Group like terms:
[tex](ab-ab)+(ac-ac)+(abc-abc)+(cb-cb)[/tex]
Anything subtracted from itself is 0.
Simplify:
[tex]0+0+0+0\\0[/tex]
