How do you use the binomial series to expand #(1 - 4x)^8#?

1 Answer
Mar 7, 2017

Answer:

Using a calculator to plug in to the Binomial Theorem.

Explanation:

Using the formula #(a+b)^n = sum_(k = 0)^n ((n),(k))"(a^(n-k)b^k)#, plug in:

#(1-4x)^8 = sum_(k = 0)^8 (nCr(8,{0,1,2,3,4,5,6,7,8}) (1^(8-k)b^k)#
= #sum_(k = 0)^8 {1,8,28,56,70,56,28,8,1} (1^(8-k)b^k)#

=

# {-1.55315_E15,-1.24252_E16,-4.34881_E16,-8.69761_E16,-1.0873_E17,-8.69761_E16,-4.34881_E16,-1.24252_E16,-1.55315_E15}#