Question

Which is true about the degree of the sum and difference of the polynomials 3x5y – 2x3y4 – 7xy3 and –8x5y + 2x3y4 + xy3? Both the sum and difference have a degree of 6. Both the sum and difference have a degree of 7. The sum has a degree of 6, but the difference has a degree of 7. The sum has a degree of 7, but the difference has a degree of 6.

Answer 1

The correct answer is C) The sum has a degree of 6, but the difference has a degree of 7.

In order to find the correct answer, we first have to find the sum and difference. We'll start with the sum.

3x^5y - 2x^3y^4 - 7xy^3 - 8x^5y + 2x^3y^4 + xy^3

By combining like terms we get the following.

-5x^5y -6xy^3

The term with the most amount of variables is the first one which has 5 x's and 1 y. As a result, it is a 6th degree polynomial.

For the difference, we have the following.

3x^5y - 2x^3y^4 - 7xy^3 - (-8x^5y + 2x^3y^4 + xy^3)

Which simplifies to

11x^5y - 4x^3y^4 -8xy^3

The term in this final simplification with the most variables is the second one, with 3 x's and 4 y's. As a result, there are 7 variables and it is a 7th degree.

Answer 2

Option 3 - The sum has a degree of 6, but the difference has a degree of 7.

Step-by-step explanation:

Given : Polynomials
`3x^5y - 2x^3y^4 - 7xy^3` and
`-8x^5y+ 2x^3y^4+ xy^3`

To find : Which is true about the degree of the sum and difference of the polynomials ?

Solution :

First we find the sum and the difference of the polynomials,

Sum of polynomials,

`=3x^5y - 2x^3y^4 - 7xy^3+(-8x^5y+ 2x^3y^4+ xy^3)`

`=3x^5y - 2x^3y^4 - 7xy^3-8x^5y+ 2x^3y^4+ xy^3`

`=-5x^5y-6xy^3`

The degree of the sum polynomial is 6.

Difference of polynomials,

`=3x^5y - 2x^3y^4 - 7xy^3-(-8x^5y+ 2x^3y^4+ xy^3)`

`=3x^5y - 2x^3y^4 - 7xy^3+8x^5y- 2x^3y^4- xy^3`

`=-4x^3y^4+11x^5y-8xy^3`

The degree of the difference polynomial is 7.

Therefore, The sum has a degree of 6, but the difference has a degree of 7.

So, Option 3 is correct.