((x^(2)y^(2))/(a^(2)b^(3)))^(n)

Simplify that : ((x^2\ y^2)/(a^2b^3))^n

(x+y)^(3)-(x-y)^(3) can be factorized as 2y(3x^(2)+y^(2)) (b) 2x(3x^(2)+y^(2))2y(3y^(2)+x^(2)) (d) 2x(x^(2)+3y^(2))

If x+y=a+b and x^(2)+y^(2)=a^(2)+b^(2) , then by mathematical induction prove that x^(n)+y^(n)=a^(n)+b^(n) . For all n in NN .

If S_(n)=(x+y)+(x^(2)+xy+y^(2))+(x^(3)+x^(2)y+y^(2)x+y^(3))+…n terms then prove that (x-y)S_(n)=[(x^(2)(x^(n)-1))/(x-1)-(y^(2)y^(n)-1)/(y-1)] .

If ((x^(-1)y^2)/(x^3y^(-2)))^1.\ ((x^6\ y^(-3))/(x^2\ y^3))^(1/2)=x^a y^b , prove that a+b=-1 , where x\ a n d\ y are different positive primes.

If y=x^(n){a cos(log x)+b sin(log x)}, prove that x^(2)(d^(2)y)/(dx^(2))+(1-2n)(dy)/(dx)+(1+n^(2))y=0

If (x)/(a)+(y)/(b)=2 touches the curve (x^(n))/(a^(n))+(y^(n))/(b^(n))=2 at the point (alpha,beta), then

If y=1+(x)/(1!)+(x^(2))/(2!)+(x^(3))/(3!)+ . . .+(x^(n))/(n!) , prove that (dy)/(dx)+(x^(n))/(n!)=y

The curve ((x)/(a))^(n)+((y)/(b))^(n)=2 touches the straight line (x)/(a)+(y)/(b)=2 at the point (a, b) :

The line (x)/(a)+(y)/(b)=2 touches the curve ((x)/(a))^(n)+((y)/(b))^(n)=2 at the point (a, b) for