Question

Which is true about the completely simplified differences of the polynomials a^3b+9a^2b^2-4ab^5 and a^3b-3a^2b^2+ab^5 ?

Answer 1

Answer:

Option D.

Step-by-step explanation:

The given polynomials are $a^{3}b+9a^{2}b^{2}-4ab^{5}$ and $a^{3}b-3a^{2}b^{2}+ab^{5}$

Now we will subtract the 1st polynomial from second.

$a^{3}b+9a^{2}b^{2}-4ab^{5}$ - ($a^{3}b-3a^{2}b^{2}+ab^{5}$)

= $a^{3}b-a^{3}b+9a^{2}b^{2}+3a^{2}b^{2}-4ab^{5}-ab^{5}$

= $12a^{2}b^{2}-5ab^{5}$

Now the degree of both the terms of the polynomial is

Degree of 1st term = 2 + 2 = 4

Degree of 2nd term = 1 + 5 = 6

Therefore, the highest degree of the polynomial is 6.

Option D. will be the answer.

Answer 2

Hello from MrBillDoesMath!

Answer:

Binomial with a degree of 6  (the second Choice)

Discussion:

(a^3b+9a^2b^2-4ab^5)  - (a^3b-3a^2b^2+ab^5) =

(-4ab^5- ab^5) +  ( a^3b-a^3b) + ( 9a^2b^2 + 3a^2b^2) =

(-4ab^5- ab^5) +  0                   + ( 9a^2b^2 + 3a^2b^2) =

12 a^2 b^2 - 5 a b^5

This is a binomial with degree 6 (degree of last term = 1 + 5 = 6).

Thank you,

MrB