Question

Whats 7xy+ x³-3y³-5x²y² in standard form?​

Answer 1

Standard form of the polynomial is
`x^(3)-5 x^(2) y^(2)+7 x y-3 y^(3)` or
`-3 y^(3)-5 x^(2) y^(2)+7 x y+x^(3)`.

Degree of the polynomial is 4.

Solution:

Given polynomial:

`7 x y+x^(3)-3 y^(3)-5 x^(2) y^(2)`

To write this polynomial in standard form:

`7 x y+x^(3)-3 y^(3)-5 x^(2) y^(2)`

Case 1:

Standard form of the polynomial is writing x from highest power to lowest power.

Therefore, standard form of the polynomial is

`x^(3)-5 x^(2) y^(2)+7 x y-3 y^(3)`

Case 2:

Standard form of the polynomial is writing y from highest power to lowest power.

Therefore, standard form of the polynomial is

`-3 y^(3)-5 x^(2) y^(2)+7 x y+x^(3)`

Degree of the polynomial:

The highest power of in the polynomial is the degree of the polynomial.

Here, the highest power is 2 + 2 = 4.

Hence the degree of the polynomial is 4.