1) (a + b)^{2} = a^{2} + b^{2} + 2ab2) (a - b)^{2} = a^{2} + b^{2} - 2ab3) (a + b)^{2} + (a - b)^{2} = 2(a^{2} + b^{2})4) (a + b)^{2} - (a - b)^{2} = 4ab5) (a^{2} - b^{2}) = (a - b)(a + b)6) (a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)7) (a - b)^{3} = a^{3} - b^{3} - 3ab(a - b)8) (a^{3} + b^{3}) = (a + b)(a^{2} - ab + b^{2})9) (a^{3} - b^{3}) = (a - b)(a^{2} + ab + b^{2})10) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca)11) (a^{3} + b^{3} + c^{3} - 3abc) = (a + b + c)(a^{2} + b^{2} + c^{2} - ab - bc - ca)If a + b + c = 0 then a ^{3} + b^{3} + c^{3} = 3abc12) (a + b + c + d)^{2} = [a^{2} + b^{2} + c^{2} + d^{2} + 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. |