[Math] Binomial expansion of modulus

Question

How one can perform binomial expansion of modulus of a quantity.
For example, can we expand |-1+x| ? If, yes how?
Thanks

Answer 1

start with squaring the expression because the square of any expression is positive $$\left(\vert -1+x\vert^{2}\right)^{n}=\left(-1+x\right)^{2n}.$$ Now you may use the normal binomial theorem to expand.

let $m=2n$ then expand $$\left(-1+x\right)^{m}.$$ Re substitute the $2n$ back after expansion.