Question

8mn5 – 2m6 + 5m2n4 – m3n3 + n6 – 4m6 + 9m2n4 – mn5 – 4m3n3 in standard form

Answer 1

    In a polynomial with two variables, degree of each term is calculated by the sum of exponents of each variable.

    Arrange the terms in decreasing order of the degree,

 Standard form of the given polynomial will be,

  $(-6m^6+3m^3n^3+14m^2n^4+7mn^5+n^6)$

Given polynomial is,

        $8mn^5-2m^6+5m^2n^4-m^3n^3+n^6-4m^6+9m^2n^4-mn^5-4m^3n^3$

First add the like terms of the given polynomial,

= $(8mn^5-mn^5)+(-2m^6-4m^6)+(5m^2n^4+9m^2n^4)-(m^3n^3-4m^3n^3)+n^6$

= $7mn^5-6m^6+14m^2n^4+3m^3n^3+n^6$

Degree of each term from left to right is 6.

Therefore, go by alphabetically (m first then n) with the largest degree in each term,

Standard form of the polynomial will be,

  $(-6m^6+3m^3n^3+14m^2n^4+7mn^5+n^6)$

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