Add: `4x^2y,-3xy^2,5xy^2,5x^2y`

Simplify combining like terms: 5x^2y-5x^2+3yx^2-3y^2+x^2+8xy^2-3y^2

Identify like terms in the following: xy^2,-4yx^2,2xy^2,7y,-11x^2-100x,-11yx,20x^2y,-6x^2y,2xy,3x

Classify the following polynomials as monomials,binomials,trinomials.Which polynomials do not fit in any of these three categories: x+y ,1000, x+ x^2 +x^3 +x^4 , 7+y+2x , 2y-3y^2 , 2y-3y^2 +4y^3 , 5x-2y+3xy , 4z-15z^2 , ab+bc+cd+da, pqr, p^2q +pq^2 ,2p+2q

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

The solution of x^(2)dy-y^(2)dx+xy^(2)(x-y)dy=0, is

Using Properties of determinants, prove that: {:|(x^2+1,xy,yz),(xy,y^2+1,yz),(xz,yz,z^2+1)|=1+x^2+y^2+z^2

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)

What should be taken away from 3x^2-4y^2+5xy+20 to obtain -x^2-y^2+6xy+20 ?

Distance between the parallel lines 4x^2 +20xy +25y^2+2x+5y -12 = 0

If x and y are positive integers such that, xy+x+y=71,x^2 y+xy^2=880 , then x^2+y^2 =