Question

Which polynomial correctly combines the like terms and expresses the given polynomial in standard form?

Answer 1

Answer:

option (d) is correct.

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

Step-by-step explanation:

Given polynomial,

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

We have to combine like terms and rewrite the polynomial in standard form,

Standard form of a polynomial refers to the writing each term in increasing order of degreethat is from highest to lowest degree.

First we combine like terms,

Here, $8mn^5$ and $-mn^5$ has same power. so adding them we get, $7mn^5$

Similarly,$-2m^6-4m^6=-6m^6$

also, $+5m^2n^4+9m^2n^4=14m^2n^4$

also, $-m^3n^3-4m^3n^3=-5m^3n^3$

Thus, when we add all term and writing again in standard form, we get,

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

Thus, option (d) is correct.

Answer 2

Answer:

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

Step-by-step explanation:

The given polynomial is 8mn^5  -2m^6 +5m^2 n^4 - m^3 n^3 + n^6 - 4m^6 + 9m^2n^4 -mn^5 - 4m^3n^3

Now we have to identify the like terms and simplify.

Like terms are nothing but the terms which have the same variables with same powers.

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

Now combine the like terms

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

It can be written in standard form

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

The answer is D)

Hope this will helpful.

Thank you.