`(2/x - y)^4` Use the Binomial Theorem to expand and simplify the expression.

You need to use the binomial formula, such that:

`(x+y)^n = sum_(k=0)^n ((n),(k)) x^(n-k) y^k`

You need to replace `2/x` for x, y for y and 4 for n, such that:

`(2/x - y)^4 = 4C0 (2/x)^4+4C1 (2/x)^3*(-y)^1+4C2 (2/x)^2*(-y)^2+4C3 (2/x)^1*(-y)^3 + 4C4 3a*(-y)^4 `

By definition, nC0 = nCn = 1, hence `4C0 = 4C4 = 1.`

By definition nC1 = nC(n-1) = n, hence `4C1 = 4C3 = 4.`

By definition `nC2 = (n(n-1))/2` , hence `4C2 = 6` .

`(2/x - y)^4 = 16/(x^4)- (32y)/(x^3)+ (24y^2)/(x^2)- (8y^3)/x  + y^4 `

Hence, expanding the number using binomial theorem yields the simplified result `(2/x - y)^4 = 16/(x^4)- (32y)/(x^3)+ (24y^2)/(x^2)- (8y^3)/x  + y^4.`