Formulas And Calculations Algebra Formula: Definition, Formulas and Examples By StudyMaterialz - January 19, 2022 0 88 FacebookTwitterPinterestWhatsApp Basic Algebra Formulas Basic Algebra Formulas Algebra Identities Difference of Squares a2 – b2 = (a-b)(a+b) Difference of Cubes a3 – b3 = (a – b)(a2+ ab + b2) Sum of Cubes a3 + b3 = (a + b)(a2 – ab + b2) Special Algebra Expansions Formula for (a+b)2 and (a-b)2 (a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab +b2 Formula for (a+b)3 and (a-b)3 (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a – b)3 = a3 – 3a2b + 3ab2 – b3 Roots of Quadratic Equation Formula Consider this quadratic equation: ax2 + bx + c = 0 Where a, b and c are the leading coefficients. The roots for this quadratic equation will be: Arithmetic Progression Consider the following arithmetic progression: a + (a + d) + (a + 2d) + (a + 3d) + … Where: a is the initial term d is the common difference The nth term The nth term, Tn of the arithmetic progression is: Tn = a + (n – 1)d Sum of the first n term The sum of the first n terms of the arithmetic progression is: Geometric Progression Consider the following geometric progression: a + ar + ar2 + ar3 + … Where: a is the scale factor r is the common ratio The nth term The nth term, Tn of the geometric progression is: Tn = ar n – 1 Sum of the first n terms The sum of the first n terms, Sn is: The sum to infinity If -1 < r < 1, the sum to infinity, S∞ is: READ HERE Factoring and Product Formulas