Question

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

Answer 1

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}#