ABSTRACT
At the end of this chapter, you should be able to:
• define a binomial expression • use Pascal’s triangle to expand a binomial expression • state the general binomial expansion of (a + x)n and (1 + x)n • use the binomial series to expand expressions of the form (a + x)n for positive, negative and fractional
values of n • determine the r ’th term of a binomial expansion • use the binomial expansion with practical applications
A binomial expression is one that contains two terms connected by a plus or minus sign. Thus (p +q), (a +x)2, (2x + y)3 are examples of binomial expression. Expanding (a +x)n for integer values of n from 0 to 6 gives the results shown at the top of page 135. From the results the following patterns emerge:
(i) ‘a’ decreases in power moving from left to right. (ii) ‘x’ increases in power moving from left to right.
