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.

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.

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

Step-by-step explanation:  

Given : Polynomials and

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,

The degree of the sum polynomial is 6.

Difference of polynomials,

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.