[0],[" (ii) "(x+y-2z)^(2)-x^(2)-y^(2)-3x^(2)+4xy]

Simplify: (x+y-2z)^(2)-x^(2)-y^(2)-3z^(2)+4xy

Simplify each of the following expressions: (x+y+z)^(2)+(x+(y)/(2)+(z)/(3))^(2)-((x)/(2)+(y)/(3)+(z)/(4))^(2)(x+y-2z)^(2)-x^(2)-y^(2)-3z^(2)+4xy-(x^(2)+x+1)^(2)-(x^(2)+x+1)^(2)

Find the following products: z^(2)+2)(z^(2)-3) (ii) (3x-4y)(2x-4y)(3x^(2)-4xy)(3x^(2)-3xy)( iv )(x+(1)/(5))(x+5)

Add the algebraic expressions: 4xy^(2)-7x^(2)y,12x^(2)y-6xy^(2),-3x^(2)y+5xy^(2)

Find the following produts: (i) (x+y+2z)(x^(2)+y^(2)+4z^(2)-xy-2yz-2xz)(2x-y+2z)(4x^(2)+y^(2)+9z^(2)+2xy+3yz-6xz)

Subtract: (i) -8xy from 7xy (ii) x^(2) from -3x^(2) (iii) (x - y) from (4y - 5x) (iv) (a^(2) + b^(2) - 2ab) from (a^(2) + b^(2) + 2ab) (v) (x^(2) - y^(2)) from (2x^(2) - 3y^(2) + 6xy) (vi) (x -y + 3z) from (2z - x - 3y)

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

Prove that |(x^(2),x^(2)-(y-z)^(2),yz),(y^(2),y^(2)-(z-x)^(2),zx),(z^(2),z^(2)-(x-y)^(2),xy)|=(x-y)(y-z)(z-x)(x+y+z)(x^(2) + y^(2) + z^(2)) .

Solution of D.E (dy)/(dx)=(2x+5y)/(2y-5x+3) is,if (y(0)=0) (1) x^(2)-y^(2)+5xy-3y=0 (2) x^(2)+y^(2)+5xy-3y=0 (3) x^(2)-y^(2)+5xy+3y=0 (4) x^(2)-y^(2)-5xy-3y=0