Answer
$=y^4-16y^3+96y^2-256y+256$
Work Step by Step
Binomial Theorem or Binomial expansion can be defined as:
$(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$
Need to apply the formula to get the Binomial Expansion.
we have
$(y-4)^4=\displaystyle \binom{4}{0}(y)^4(-4)^0+\displaystyle \binom{4}{1}(y)^3(-4)^1+\displaystyle \binom{4}{2}(y)^2(-4)^2+\displaystyle \binom{4}{3}(y)^1(-4)^3+\displaystyle \binom{4}{4}(y)^0(-4)^4$
$=(y^4)(1)+(4)(y^3)(-4)+(6)(y^2)(16)+(4)(y)(-64)+(256)(1)$$\bf{(Simplify)}$
$=y^4-16y^3+96y^2-256y+256$
