Basic Algebra FormulasA Quick Guide for the Algebra NerdHere is a quick guide of basic algebra formulas that you may use for quick reference. Lets get started with exponents Exponent Formulas (a^m)(a^n) = a^(m+n) (ab)^m = a^m*b^m (a^m)^n = a^(mn) a^(m/n) = (a^m)^(1/n) a^0 = 1 (a^m)/(a^n) = a^(m-n) a^(-m) = 1/a^m These are some of the basic rules involved in problems based on exponents. We will get into some more later in another article but this set is a handy guide to be placed here in this quick reference section. Logarithm loga(x/y) = loga (x) loga (y) loga (xy) = loga (x) + loga (y) loga (xr) = rloga (x) loga (ax) = x loga (a) = 1 ln (x) = loge (x) log (x) = log10 x aloga(x) = x loga(1) = 0 Binomial Theorem Check out these handy basic algebra formulas from the binomial theorem. (a + b)^1 = a + b (a + b)^2 = a^2 + 2ab + b^2 (a + b)^3 = a^3 + 3 a^2b + 3ab^2 + b^3 (a + b)^4 = a^4 + 4(a^3)b + 6(a^2)(b^2)+ 4 ab^3 + b4 (a b)^2 = a^2 2ab + b^2 a^2 b^2 = (a + b)(a b) (a b)^3 = a^3 3(a^2)b + 3a (b^2) b^3 a^3 b^3 = (a b)(a^2 + ab + b^2) a^3 + b^3 = (a + b)(a^2 + ab + b^2) That should take care of your binomial theorem needs for the time being. Dealing with Zero Zero is considered to be one of the most important discoveries by mankind. Its special, its intriguing and above all 0/a = 0 0 can never be the denominator. a/0 is undefined. a^0 = 1 0^a = 0 a*0 = 0 Inequalities Here is a set of rules that will see you through tough times with inequalities. If a > b and b > c, then a > c If a > b, then a + c > b + c If a > b, then ac > bc when c > 0 If a > b and c < 0, then ac < bc We will be consistently adding to this database of basic algebra formulas. So do not forget to bookmark this page as one of your favourites.
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