Question 1043966
{{{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}}}


Several use of number property arrangements allows the advantage of Difference of Two Squares.
{{{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}}}
{{{(a+b+c)(a+b-c)(-a+b+c)(a-b+c)}}}
{{{(a+b+c)(a+b-c)(-1)(a-b-c)(a-b+c)}}}
{{{((a+b)+c)((a+b)-c)(-1)((a-b)-c)((a-b)+c)}}}
{{{((a+b)^2-c^2)(-1)((a-b)^2-c^2)}}}


{{{(a^2+2ab+b^2-c^2)(-1)(a^2-2ab+b^2-c^2)}}}
{{{(-1)(a^2+2ab+b^2-c^2)(a^2-2ab+b^2-c^2)}}}-----Either this one or
{{{(-1)(a^2+b^2+2ab-c^2)(a^2+b^2-2ab-c^2)}}}-----this one would be best
done using a lattice arrangement for multiplying.    


Sixteen terms initially occur and a few of them drop due to additive inverses.


{{{(-1)(a^4+a^2b^2+a^2b^2+b^4-a^2c^2-a^2c^2-4a^2b^2+c^4)}}}
{{{(-1)(a^4+b^4+c^4-2a^2b^2-2a^2c^2)}}}
{{{highlight(-a^4-b^4-c^4+2a^2b^2+2a^2c^2)}}}-----Or this can be arranged for neatness of indicating the additions of terms.