Algebra Cheat Sheet - Algebra II - Intermediate |, Study notes of Algebra

Download Algebra Cheat Sheet - Algebra II - Intermediate | and more Study notes Algebra in PDF only on Docsity! Arithmetic Operations ab + ac = a (b + c ) a Algebra Cheat Sheet Basic Properties & Facts Properties of Inequalities If a<bthena+c<b+cand a−c<b−c If a<bandc>0 then ac<bcand a<b cc If a < b and c < 0 then ac > bc and a > b cc Properties of Absolute Value b a = = c bc b b  c a+c =ad+bc a−c =ad−bc bd bd a =a ifa≥0 bd bd −a ifa<0 a  b  = ab  c c a ac  a + b = a + b a ≥ 0 −a = a a − b = b − a c−dd−c ccc ab=ab a=a ab+ac a bb b ad =b+c, a=0 Exponent Properties  = a+b≤a+b TriangleInequality c bc Distance Formula a a  a −n  b n (a + bi)+ (c + di) = a + c + (b + d )i am = am = a (a+bi)−(c+di)=a−c+(b−d)i a m d  nmn+m IfP =(x,y )andP =(x ,y )aretwo ann−m1 111 222 = a (an) =anm n (ab) =anbn a−n = 1 an am = a = am−n a0 =1, a=0 points the distance between them is d(P,P)= (x−x)2+(y−y)2 122121 Complex Numbers i= −1 i2 =−1 −a=i a, a≥0 bn   =  = n n 1 ()() b a a Properties of Radicals (a+bi)(c+di)= ac−bd +(ad +bc)i (a+bi)(a−bi)=a2 +b2