Simplify : `(x-2y)(x^2-2y)+(y+2x)(x^2+4y)-(3x-2y)(x^2-4y)`.

Simplify the following : (x-y)(2y-x)+(x+y)(x-y)-(y-3x)(2x-3y)

Simplify the following : (x - y)(y - x) + (x + y)(x - 2y)

Simplify the following:(x-2y) (y-3x)+(x+y) (x-3y)- (y-3x)(4x-5y).

If S=(x+y)(x-y)+(1)/(2!)(x+y)(x-y)(x^(2)+y^(2))+(1)/(3!)(x+y)(x-y)(x^(4)+y^(4)+x^(2)y^(2))+..., then S =

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0

The degree of the polynomial (x^2 + 2x^3) (x^2 -5x^2y^2 + y^4) is

The centre of the cirlces cutting three circles x^2+y^2-2x-4y+4=0, x^2+y^2-4x-6y+4=0, x^2+y^2-4x-8y+4=0 orthogonally is

I : If y=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...." then "x=y+(y^(2))/(2!)+(y^(3))/(3!)+.... II : If y=x+(x^(2))/(2)+(x^(3))/(3)+....oo,"then "x=y-(y^(2))/(2!)+(y^(3))/(3!)-(y^(4))/(4!)+....