Standard form of the polynomial is [tex]x^{3}-5 x^{2} y^{2}+7 x y-3 y^{3}[/tex] or [tex]-3 y^{3}-5 x^{2} y^{2}+7 x y+x^{3}[/tex].
Degree of the polynomial is 4.
Solution:
Given polynomial:
[tex]7 x y+x^{3}-3 y^{3}-5 x^{2} y^{2}[/tex]
To write this polynomial in standard form:
[tex]7 x y+x^{3}-3 y^{3}-5 x^{2} y^{2}[/tex]
Case 1:
Standard form of the polynomial is writing x from highest power to lowest power.
Therefore, standard form of the polynomial is
[tex]x^{3}-5 x^{2} y^{2}+7 x y-3 y^{3}[/tex]
Case 2:
Standard form of the polynomial is writing y from highest power to lowest power.
Therefore, standard form of the polynomial is
[tex]-3 y^{3}-5 x^{2} y^{2}+7 x y+x^{3}[/tex]
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.
