Question

find solutions of

256x^4=(x-8)^4

Answer 1

There might be a few approaches to this question, but it depends on what topic you're learning, I guess.

One "nasty" one could be to expand the right hand side (the binomial theorem could help you here!) and then bring everything to one side of the equation and try to factorise again.
Another method could be to draw the graphs of the left and right hand sides as if they were two different functions, estimate a point of intersection, then expand (again, binomial theorem might help) but after you expand, DIFFERENTIATE what you get and use Newton's Method of Approximation with lots of iterations to find the root.
Another method could be to use the difference of two squares formula.

Can you think of another method? Do any of these methods seem attractive? If you don't know what the binomial theorem, Newton's Method or the difference of two squares are, you can look them up (Google is your friend) and learn some new, useful methods :D

Answer 2

ok, i used wolfram alpha and got the answer. it turns into x = 4 diff answers. if you could explain maybe the simplest way to figure it out, that would be wonderful.