Each expression is factored using appropriate algebraic identities. For perfect square trinomials, we use (a ± b)² = a² ± 2ab + b². For difference of squares, we use a² - b² = (a + b)(a - b). For sum/difference of cubes, we use a³ ± b³ = (a ± b)(a² ∓ ab + b²). For expressions fitting the pattern a³ + b³ + c³ - 3abc, we use the identity (a + b + c)(a² + b² + c² - ab - bc - ca).