Question

Write the expression thats in the comments, in the form (a+b)^n

Answer 1

\[1024x ^{10}-3840x^8+5760x^6-4320x^4+1620x^2-243\]

Answer 2

@PaxPolaris

Answer 3

How would i go about doing putting it into that form?

Answer 4

any idea?

Answer 5

looks like the answer involves imaginary numbers .. if even possible ...?

Answer 6

it is possible

Answer 7

if, \[\large a^{10}=1024x^{10}\implies a=2x\cdot e^{\pi i n /5}\]

\[\large b^{10}=-3^5 \implies b=\sqrt3i \cdot e^{\pi i n/5}= \sqrt3e^{i \cdot \pi(2n-5)/10}\]

can't see how \(10a^9b\) can be 0