$ab(b - c) + ac(c - b) - a(b^2 - 3bc + c^2) = abc$
$ab^2 - abc + ac^2 - abc - ab^2 + 3abc - ac^2 = abc$
$(ab^2 - ab^2) + (ac^2 - ac^2) + (-abc - abc + 3abc) = abc$
0 + 0 + abc = abc
abc = abc

$4a(a + b) - a(3a - 4b) - 8ab = a^2$
$4a^2 + 4ab - 3a^2 + 4ab = a^2$
$(4a^2 - 3a^2) + (4ab - 4ab) = a^2$
$a^2 + 0 = a^2$
$a^2 = a^2$

$a(a + 2b) + b(a + b) = b(2a + b) + a(a + b)$
$a^2 + 2ab + ab + b^2 = 2ab + b^2 + a^2 + ab$
$a^2 + 3ab + b^2 = a^2 + 3ab + b^2$

a(b + c − bc) − b(a + c − ac) = (a − b)c
ab + ac − abc − ab − bc + abc = ac − bc
(ab − ab) + (abc − abc) + ac − bc = ac − bc
0 + 0 + ac − bc = ac − bc
ac − bc = ac − bc