|
1) (a + b)2 = a2 + b2 + 2ab 2) (a - b)2 = a2 + b2 - 2ab 3) (a + b)2 + (a - b)2 = 2(a2 + b2) 4) (a + b)2 - (a - b)2 = 4ab 5) (a2 - b2) = (a - b)(a + b) 6) (a + b)3 = a3 + b3 + 3ab(a + b) 7) (a - b)3 = a3 - b3 - 3ab(a - b) 8) (a3 + b3) = (a + b)(a2 - ab + b2) 9) (a3 - b3) = (a - b)(a2 + ab + b2) 10) (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) 11) (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ca) If a + b + c = 0 then a3 + b3 + c3 = 3abc 12) (a + b + c + d)2 = [a2 + b2 + c2 + d2 + 2a(b + c + d) + 2b(c + d) + 2cd] Linear Equation in one variableGeneral form of a linear equation in one variable is ax + b = 0, where a, b are real numbers and a ≠ 0.Examples of linear equations in one variable: 2x + 5 = 0, 3x - 4 = 0 Linear Equations in two variablesGeneral form of a linear equation in two variable is ax + by = c where a, b, c are real numbers and a ≠ 0, b ≠ 0.Examples of linear equations in two variables: 2x + 3y = - 5, 3x - 4y = 7 In order to solve a linear equation in 'n' variables we need atleast 'n' equations. |