3.12.3: Formula Review Last updated Save as PDF Page ID 129537 OpenStax OpenStax Formula Review 3.4 Rational Numbers a c ± b c = a ± b c a c ± b c = a ± b c a b × c d = a × c b × d a b × c d = a × c b × d a b × c d = a × c b × d a b ÷ c d = a d × d c = a × d b × c a b × c d = a × c b × d a b ÷ c d = a d × d c = a × d b × c 3.5 Irrational Numbers a × b = a × b a × b = a × b a × x ± b × x = ( a ± b ) × x a × x ± b × x = ( a ± b ) × x a ÷ b = a b = a b a ÷ b = a b = a b a 2 − b 2 = ( a − b ) ( a + b ) a 2 − b 2 = ( a − b ) ( a + b ) 3.6 Real Numbers a × ( b + c ) = a × b + a × c a × ( b + c ) = a × b + a × c a + b = b + a a + b = b + a a × b = b × a a × b = b × a a + ( b + c ) = ( a + b ) + c a + ( b + c ) = ( a + b ) + c a × ( b × c ) = ( a × b ) × c a × ( b × c ) = ( a × b ) × c a + 0 = a a + 0 = a a × 1 = a a × 1 = a a + ( − a ) = 0 a + ( − a ) = 0 a × ( 1 a ) = 1 a × ( 1 a ) = 1 3.8 Exponents a n a m = a n + m a n a m = a n + m a n a m = a ( n − m ) a n a m = a ( n − m ) a 0 = 1 a 0 = 1 , provided that a ≠ 0 a ≠ 0 ( a × b ) n = a n × b n ( a × b ) n = a n × b n ( a b ) n = a n b n ( a b ) n = a n b n ( a n ) m = a ( n × m ) ( a n ) m = a ( n × m ) a − n = 1 a n a − n = 1 a n , provided that a ≠ 0 a ≠ 0 3.10 Arithmetic Sequences a i = a 1 + d × ( i − 1 ) a i = a 1 + d × ( i − 1 ) d = a j − a i j − i d = a j − a i j − i a 1 = a i − d ( i − 1 ) a 1 = a i − d ( i − 1 ) s n = n ( a 1 + a n 2 ) s n = n ( a 1 + a n 2 ) 3.11 Geometric Sequences a n = a 1 r n − 1 a n = a 1 r n − 1 s n = a 1 ( 1 − r n − 1 1 − r ) s n = a 1 ( 1 − r n − 1 1 − r ) 3.11 Geometric Sequences a n = a 1 r n − 1 a n = a 1 r n − 1 s n = a 1 ( 1 − r n − 1 1 − r ) s n = a 1 ( 1 − r n − 1 1 − r )