Carry out the following divisions: `34x^3y^3z^3 :- 51xy^2z^3`

Carry out the following divisions: -36y^3 :-9y^2

Workout the following division: 9x^2y^2(3z-24):-27xy(z-8)

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)

Find the common factors of the given terms 3x^2y^3 , 10x^3y^2 , x^2y^2z .

Find the shortest distance between the following pair of lines : (x-1)/(2) = (y-2)/(3)=(z-3)/(4),(x-2)/(3)=(y-3)/(4)=(z-5)/(5)

Using matrices, solve the following system of linear equations: x-y+z=4,2x+y-3z=0,x+y+z=2

Divide the given polynomial by the given monomial: 8(x^3y^2z^2 +x^2y^3z^2+x^2y^2z^3):-4x^2y^2z^2

Find the value of x, y and z from the following equations: (i) [(4,3),(x,5)]=[(y,z),(1,5)] (ii) [(x+y, 2 ),(5+z, xy)]=[(6,2),(5,8)] (iii) [(x+y+z),(x+z), (y+z)]=[(9),(5),(7)]