[" Tif "(2x+y)+2x-y times4x^(2)+y^(2))],[" (uy) "(x-(y)/(6)-1)(x+(y)/(b)+1)]

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

Factorize each of the following algebraic expressions: (1) (x-y)^2+(x-y) (2) 6(a+2b)-4(a+2b)^2 (3) a(x-y)+2b(y-x)+c(x-y)^2 (4) -4\ (x-2y)^2+8(x-2y)

[" The solution of "(dy)/(dx)=(1)/(2x-y^(2))" is given by "],[[" (A) "y=Ce^(-2x)+(1)/(4)x^(2)+(1)/(2)x+(1)/(4)," (B) "x=Ce^(-y)+(1)/(4)y^(2)+(1)/(4)y+(1)/(2)],[" (C) "x=Ce^(y)+(1)/(4)y^(2)+y+(1)/(2)," (D) "x=Ce^(2y)+(1)/(2)y^(2)+(1)/(2)y+(1)/(4)]]

{:("Column" A ,, "Column" B), (225x^(2) - 625 y^(2) = ,, (a) 25(x-2) (x-2)), (x^(2) - x - y - y^(2) = ,, (b) 25(3x- 5y) (3x + 5y)), (x^(2) - x - y^(2) + y = ,, (x + y) (x - y- 1)), (25x^(2) - 100 x + 100 = ,, (d) (x - y) (x + y -1)), (,,(e) (x + y) (x + y - 1)):}

If the circle x^(2)+y^(2)=a^(2) intersects the hyperbola xy=c^(2) in four points P (x_(1) ,y_(1)) Q (x_(2), y_(2)) R (x_(3) ,y_(3)) S (x_(4) ,y_(4)) then 1) x_(1)+x_(2)+x_(3)+x_(4)=2c^(2) 2) y_(1)+y_(2)+y_(3)+y_(4)=0 3) x_(1)x_(2)x_(3)x_(4)=2c^(4) 4) y_(1)y_(2)y_(3)y_(4)=2c^(4)

If (x+y): (x-y)= 4:1, then find the ratio (x^(2)+y^(2)):(x^(2)-y^(2))

The factors of x^(3)-1+y^(3)+3xy are (a) (x-1+y)(x^(2)+1+y^(2)+x+y-xy)( b) (x+y+1)(x^(2)+y^(2)+1-xy-x-y)( c) (x-1+y)(x^(2)-1-y^(2)+x+y+xy)(d)3(x+y-1)(x^(2)+y^(2)-1)

Orthogonal trajectories of the family of curves represented by x^(2)+2y^(2)-y+c=0 is (A) y^(2)=a(4x-1)(B)y^(2)=a(4x^(2)-1)(C)x^(2)=a(4y-1)(D)x^(2)=a(4y^(2)-1)