Question

How do you use the binomial series to expand `(x – 2)^5`?

Answer 1

Us the pascal's triangle to find the answer easily:

:

`rarr(a+b)^5=1a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+1b^5`

`rarr(x-2)^5`

`=1(x^5)+5(x^4)(-2)+10(x^3)(-2^2)+10(x^2)(-2^3)+5x(-2^4)+(-2^5)`

`=x^5+5x^4(-2)+10x^3(-2^2)+10x^2(-2^3)+5x(-2^4)+(-2^5)`

`=x^5+5x^4(-2)+10x^3(4)+10x^2(-8)+5x(16)+(-32)`

`=x^5-10x^4+40x^3-80x^2+80x-32`