`x^3-7x^2+2x-3,\ 2+1/2y-3/2y^2+4y^3` are cubic polynomials True/False ?.

2-3/4x ,1/2+3/5y ,2+3a etc. are linear polynomials True/False ?.

2x^2-3x+4,\ 2-x+x^2,\ 2y^2-3/2y+1/4 are quadratic polynomials.

3-2x^2+4x^2y+8y-5/3x y^2 is a polynomial in two variables x and y .

Add the following expressions: (i) x^3-2x^2y+3x y^2-y^3,\ 2x^3-5x y^2+3x^2y-4y^3 (ii) a^2-2a^3b+3a b^3+4a^2b^2+3b^4,-2a^2-5a b^3+7a^3b-6a^2b^2+b^4

In the algebraic expression 5x^2y+7x y^2-3x y-4y x^2, we have 5x^2y and -4y x^2 as like terms, whereas 7x y^2 and -3x y are unlike terms.

State true or false : 7x^(3)+2x^(2)+3x-5 is a polynomial

Subtract: 6x^3-7x^2+5x-3 from 4-5x+6x^2-8x^3 x^3+2x^2y+6x y^2-y^3 from y^3-3x y^2-4x^2y

If A(x_1, y_1),B(x_2, y_2) and C(x_3,y_3) are vertices of an equilateral triangle whose each side is equal to a , then prove that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=3a^4

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 + 5x, 2y - 3y^2, 2y - 3y^2 + 4y^3, 5x -4y + 3xy, 4z - 15z^2, ab + bc +cd + da, pqr, p^2q + pq^2, 2p + 2q

Write down 7x y^2X\ 3x^2y\ X\ 5y^4 in the exponential form.