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Algebra cheat sheet

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Algebra Cheat Sheet Basic Properties & Facts Arithmetic Operations Properties of Inequalities If a < b then a + c < b + c and a - c < b - c a b If a < b and c > 0 then ac < bc and < c c a b If a < b and c < 0 then ac > bc and > c c æ b ö ab aç ÷ = ècø c ab + ac = a ( b + c ) æaö ç ÷ a èbø = c bc a ac = æbö b ç ÷ ècø a c ad + bc + = b d bd a c ad - bc - = b d bd a -b b-a = c-d d -c a+b a b = + c c c æaö ç ÷ ad èbø = æ c ö bc ç ÷ èdø ab + ac = b + c, a ¹ 0 a Properties of Absolute Value if a ³ 0 ìa a =í if a < 0 î -a a ³0 -a = a a+b £ a + b a n a m = a n+m an 1 = a n-m = m-n m a a (a ) a 0 = 1, a ¹ 0 ( ab ) n a -n = æaö ç ÷ èbø -n = a nm n 1 an n bn æbö =ç ÷ = n a èaø n m 1 a = an m n a = nm a ( x2 - x1 ) + ( y2 - y1 ) 2 2 n Complex Numbers i = -1 ( ) = (a ) a = a Properties of Radicals n d ( P1 , P2 ) = a æaö ç ÷ = n b èbø 1 = an -n a = a nb n Triangle Inequality Distance Formula If P1 = ( x1 , y1 ) and P2 = ( x2 , y2 ) are two points the distance between them is Exponent Properties n m a a = b b ab = a b 1 m n n 1 m i 2 = -1 -a = i a , a ³ 0 ( a + bi ) + ( c + di ) = a + c + ...
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