The square of a binomial is given by the formula (a + b)^2 = a^2 + 2ab + b^2. This formula is extensively used in algebra and is applied in finding the areas of squares and rectangles, factoring quadratic equations, and calculating probability distributions. The square of a trinomial is given by the formula (a +b +c)^2 =a^2 + b2 + c^2 + 2ab + 2ac + 2bc. It is used in algebra to factorize polynomials and perform calculations related to geometry and physics.