Answer
$y^4-16y^3+96y^2-256y+256$
Work Step by Step
According to the Binomial Theorem or Binomial expansion, the expansion for $(x+y)$ in the any number of power can be calculated as:
$(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$
Let's see how this formula works:
$(y-4)^4=\displaystyle \binom{4}{0}(y)^4(-4)^0+\displaystyle \binom{4}{1}(y)^3(-4)^1+\displaystyle \binom{4}{2}(y)^2(-4)^2+\displaystyle \binom{4}{3}(y)^1(-4)^3+\displaystyle \binom{4}{4}(y)^0(-4)^4$
or, $=y^4+4(y^3)(-4)+6(y^2)(16)+4(y)(-64)+256$
or, $=y^4-16y^3+96y^2-256y+256$
