If `x+y=1`,show that `D^n(x^ny^n)=n![y^n-(nC_1)^2 y^(n-1) x+(nC_2)^2 y^(n-2) x^2+.....+(-1)^n x^n]`

If x + y = 1, show that D ^ (n) (x ^ (n) y ^ (n)) = n! [Y ^ (n) - (nC_ (1)) ^ (2) y ^ (n -1) x + (nC_ (2)) ^ (2) y ^ (n-2) x ^ (2) + ...... + (- 1) ^ (n) x ^ (n)]

(x^(2^(n-1))+y^(2^(n-1)))(x^(2^(n-1))-y^(2^(n-1)))=

x^n - y^n = (x-y) (x^(n-1) + x^(n-2) y + … + xy^(n-2) + y^(n-1)) , x,y in R

If x+y=1, prove that sum_(r=0)^n .^nC_r x^r y^(n-r) = 1 .

If x+y=1, prove that sum_(r=0)^n .^nC_r x^r y^(n-r) = 1 .

(x^(2^n)-y^(2^n))/(x^(2^(n-1))+y^(2^(n-1)))=

If x+y=1, prove that sum_(r=0)^(n)nC_(r)x^(r)y^(n-r)

(n+2)nC_0(2^(n+1))-(n+1)nC_1(2^(n))+(n)nC_2(2^(n-1))-.... is equal to

If y=x^(2)e^(x) ,show that y_(n)=(1)/(2)n(n-1)y_(2)-n(n-2)y_(1)+(1)/(2)(n-1)(n-2)}