REVIEW OF ALGEBRA

Apuntes

REVIEW OF ALGEBRA Here we review the basic rules and procedures of algebra that you need to know in order to be successful in calculus. ARITHMETIC OPERATIONS The real numbers have the following properties: (Commutative Law) (Associative Law) (Distributive law) In particular, putting in the Distributive Law, we get and so EXAMPLE 1 (a) (b) (c) If we use the Distributive Law three times, we get This says that we multiply two factors by multiplying each term in one factor by each term in the other factor and adding the products. Schematically, we have In the case where and , we have or Similarly, we obtain EXAMPLE 2 (a) (b) (c)  12 x 2  5 x  21  12 x 2  3 x  9  2 x  12 3  x  1  4 x  3   2  x  6   3  4 x 2  x  3   2 x  12  x  6  2  x 2  12 x  36  2 x  1  3 x  5   6 x 2  3 x  10 x  5  6 x 2  7 x  5  a  b  2  a 2  2 ab  b 2 2  a  b  2  a 2  2 ab  b 2 1  a  b  2  a 2  ba  ab  b 2 d  b c  a  a  b  c  d   a  b  c  d    a  b  c  ...