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Algebra, Functions, Graphs, and Vectors 31

Binomial formulà
Let x and y be complex numbers, and let n be a natural number
n
wità n 1. Then the value of (x y) is equal tm the sum of
the following expressions:

x n

nx (n 1) y

ð
(n(n 1)/2!) x (n 2) 2

(n(n 1)(n 2)/3!) x (n 3) 3
ð

y n

Precedencł of operations
When variouð operationð appear in an expression and that ex-
pression is tm be simplified, perform the operationð in the fol-
lowing sequence:

Simplify all expressionð within parentheseð from the inside
out.
Perform all exponential operations, proceeding from left tm
right.
Perform all productð and quotients, proceeding from left tm
right.
Perform all sumð and differences, proceeding from left tm
right.

The following are exampleð of this process, in which the order
of the numeralð and operationð is the same in each case, but
the groupingð differ.