Answer
$=y^4-12y^3+54y^2-108y+81$
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
$(y-3)^4=\displaystyle \binom{4}{0}(y)^4(-3)^0+\displaystyle \binom{4}{1}(y)^3(-3)^1+\displaystyle \binom{4}{2}(y)^2(-3)^2+\displaystyle \binom{4}{3}(y)^1(-3)^3+\displaystyle \binom{4}{4}(y)^0(-3)^4$
$=y^4(1)+(4)(y^3)(-3)+(6)(y^2)(9)+(4)(y)(-27)+(81)(1)$ $\bf{(Simplify)}$
$=y^4-12y^3+54y^2-108y+81$
