[" z) "-z],[" (vii) "ab(x^(2)+y^(2))-xy(a^(2)+b^(2))]

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)

Write the coefficient of (i) x in 13x (ii) y in - 5y (iii) a in 6ab (iv) z in - 7xz (v) p in - 2 pqr (vi) y^(2) in 8xy^(2)z (vii) x^(3) in x^(3) (viii) x^(2) in -x^(2)

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

Multiply each of the monomial: (-3x^(2)y),(4xy^(2)z),(-xy^(2)z^(2)) and ((4)/(5)z)

If ax+cy+bz=X, cx+by+az=Y, bx+ay+cz=Z, show that (a^(2)+b^(2)+c^(2)-bc-ca-ab)(x^(2)+y^(2)+z^(2)-yz-zx-xy)=X^(2)+Y^(2)+Z^(2)-YZ-ZX-XY

If x/a = y/b = z/c , then show that (x^(2)-yz)/(a^(2)-bc) = (y^(2)-zx)/(b^(2) - ca) = (z^(2)-xy)/(c^(2)-ab)

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))

det[[1,x,x^(2)1,y,y^(2)1,z,z^(2)]]det[[a^(2),1,2ab^(2),1,2b1,z,z^(2)]]det[[a^(2),1,2ab^(2),1,2bc^(2),1,2c]]=det[[(a-x)^(2),(b-x^(2)),(c-x)^(2)(a-y)^(2),(b-y)^(2),(c-y)^(2)(a-z)^(2),(b-z)^(2),(c-z)^(2)]]

Prove that quad det ([yx-x^(2),zx-y^(2),xy-z^(2)zx-y^(2),xy-z^(2),yz-x^(2)xy-z^(2),yz-x^(2),zx-y^(2)]) is divisible by (x+y+z) and hence find the quotient.