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:
Option 3 - The sum has a degree of 6, but the difference has a degree of 7.
Step-by-step explanation:
Given : Polynomials [tex]3x^5y - 2x^3y^4 - 7xy^3[/tex] and [tex]-8x^5y+ 2x^3y^4+ xy^3[/tex]
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,
[tex]=3x^5y - 2x^3y^4 - 7xy^3+(-8x^5y+ 2x^3y^4+ xy^3)[/tex]
[tex]=3x^5y - 2x^3y^4 - 7xy^3-8x^5y+ 2x^3y^4+ xy^3[/tex]
[tex]=-5x^5y-6xy^3[/tex]
The degree of the sum polynomial is 6.
Difference of polynomials,
[tex]=3x^5y - 2x^3y^4 - 7xy^3-(-8x^5y+ 2x^3y^4+ xy^3)[/tex]
[tex]=3x^5y - 2x^3y^4 - 7xy^3+8x^5y- 2x^3y^4- xy^3[/tex]
[tex]=-4x^3y^4+11x^5y-8xy^3[/tex]
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.
