Special products and algebraic identities

Standard expansion and factoring identities such as (a+b)^2 = a^2+2ab+b^2, (a-b)^2, (a+b)(a-b) = a^2-b^2, (a+b)^3, a^3±b^3, and (a+b+c)^2; used to simplify expressions, reveal hidden structure, and shortcut algebraic manipulation.