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

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

Answer 2

Option D.

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.