Show that: ` (x^2+y^2)^5=(x^5-10x^3y^2+5xy^4)^2+(5x^4 y-10x^2y^3+y^5)^2 `

3x-4y=10 , 4x+3y=5

A pair of perpendicular straight lines is drawn through the origin forming with the line 2x+3y=6 an isosceles triangle right-angled at the origin. The equation to the line pair is 5x^2-24 x y-5y^2=0 5x^2-26 x y-5y^2=0 5x^2+24 x y-5y^2=0 5x^2+26 x y-5y^2=0

Multiply: (i) (2x^2-1)b y\ (4x^3+5x^2) (ii) (2x y+3y^2)(3y^2-2)

x^2\ x\ \ 2y^3\ x\ \ 5x^3y^2 is equal to: (a) 10 x^2y^5 (b) 10 x^5y^2 (c) 10 x^5y^5 (d) x^5y^5

Find the greatest common factor (GCF/HCF) of the following polynomials: 2x^3y^2,\ 10 x^2y^3 ,14 x y (ii) 14 x^3y^5,\ 10 x^5y^3,\ 2x^2y^2

Show that the equation (10x-5)^(2)+(10y-5)^(2)=(3x+4y-1)^(2) represents an ellipse, find the eccentricity of the ellipse.

Subtract: 2x^2 -5xy +3y^2+5 from 4x^2+3xy-5y^2+9

Subtract: x^2-3x y+7y^2-2 from 6x y-4x^2-y^2+5

How much bigger is 5x^(2)y^(2) - 18xy^(2) - 10x^(2)y than -5x^(2) + 6x^(2)y - 7xy ?

Given x, y in R , x^(2) + y^(2) gt 0 . Then the range of (x^(2) + y^(2))/(x^(2) + xy + 4y^(2)) is (a) ((10 - 4 sqrt(5))/(3),(10 + 4 sqrt(5))/(3)) (b) ((10 - 4 sqrt(5))/(15),(10 + 4 sqrt(5))/(15)) (c) ((5- 4 sqrt(5))/(15),(5 + 4 sqrt(5))/(15)) (d) ((20- 4 sqrt(5))/(15),(20 + 4 sqrt(5))/(15))