Class 8 Chapter 4, ( Algebraic Formulas and Equations ) Algebraic Formulas and Equations Category Formula Basic Identity (x + y)^2 = x^2 + 2xy + y^2 (x - y)^2 = x^2 - 2xy + y^2 (x + y)(x - y) = x^2 - y^2 (x + a)(x + b) = x^2 + (a+b)x + ab Cubic Identity (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3 (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3 x^3 + y^3 = (x+y)(x^2 - xy + y^2) x^3 - y^3 = (x-y)(x^2 + xy + y^2) Quadratic Equation x = (-b ± √(b^2 - 4ac)) / 2a Exponent Law a^m × a^n = a^(m+n) a^m / a^n = a^(m-n) (a^m)^n = a^(mn) a^0 = 1 (a ≠ 0) Logarithm Law log_a(mn) = log_a m + log_a n log_a(m/n) = log_a m - log_a n log_a(m^n) = n log_a m
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