Simplify `(x+y)(x^2-xy+y^2)`

Simplify (x+y)(2x+y)+(x+2y)(x-y)

Verify the following : (i) x^3+y^3=(x-y)(x^2-xy+y^2) (ii) x^3-y^3=(x-y) (x^2+xy+y^2)

Prove that |(x,y,y),(y,x,y),(y,y,x)| = (x + 2y)(x - y)^(2)

Verify x^(3)-y^(3)= (x-y)(x^(2)+y^(2)+xy) Hence factorise 216x^(3)-125y^(3)

The differential equations of all circle touching the x-axis at orgin is (a) (y^(2)-x^(2))=2xy((dy)/(dx)) (b) (x^(2)-y^(2))(dy)/(dx)=2xy ( c ) (x^(2)-y^(2))=2xy((dy)/(dx)) (d) None of these

The angle between the lines in x^(2)-xy-6y^(2)-7x+31y-18=0 is

Find (dy)/(dx) if x^(2)+xy+y^(2)=100

The point of intersection of the two lines given by 2x^2-5xy +2y^2-3x+3y+1=0 is