Answer:
6 is the degree of the sum of the polynomials
7 is the degree of the difference of the polynomials
Step-by-step explanation:
3x^5y – 2x^3y^4 – 7xy^3 and –8x^5y + 2x^3y^4 + xy^3
First we find the sum of the polynomials
[tex]3x^5y – 2x^3y^4 – 7xy^3 + –8x^5y + 2x^3y^4 + xy^3[/tex]
Combine like terms
3x^5y - 8x^5y = -5x^5y (degree = 6)
– 2x^3y^4 + 2x^3y^4 =0
– 7xy^3+ xy^3= -6xy^3 (degree= 4)
So sum of the polynomials becomes
-5x^5y -6xy^3
For degree we add the exponents
highest degree = 6
So 6 is the degree of the sum of the polynomials
Now we find the difference
[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]
Combine like terms
3x^5y + 8x^5y = 11x^5y (degree = 6)
– 2x^3y^4 - 2x^3y^4 =-4x^3y^4 (degree = 7)
– 7xy^3- xy^3= -8xy^3 (degree= 4)
So difference of the polynomials becomes
11x^5y-4x^3y^4 -8xy^3
For degree we add the exponents
highest degree = 7
So 7 is the degree of the difference of the polynomials
