Ta có
$VT = (a+b+c)(ab + bc + ca) - abc$
$= a^2b + abc + a^2c + ab^2 + b^2c + abc + abc + bc^2 + ac^2 - abc$
$= a^2b + abc + a^2c + ab^2 + b^2c + abc + bc^2 + ac^2$
$= (a^2b + a^2c) + (ab^2 + abc) + (ac^2 + abc) + (b^2c + bc^2)$
$= a^2(b+c) + ab(b+c) + ac(b+c) + bc(b+c)$
$= (b+c)(a^2 + ab + ac + bc)$
$= (b+c)[(a^2+ab) + (ac+bc)]$
$= (b+c)[a(a+b) + c(a+b)]$
$= (b+c)(a+b)(c+a) = VP$.