Question

Which is true about the degree of the sum and difference of the polynomials 3x5y – 2x3y4 – 7xy3 and –8x5y + 2x3y4 + xy3?

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Answer:

The option " The sum has degree of 6 , but the difference has a degree of 7 " is correct.

Step-by-step explanation:

Given that the sum and difference of the polynomials $3x^5y-2x^3y^4-7xy^3$ and $-8x^5y+2x^3y^4+xy^3$

Now sum the given polynomials :

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

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

$=-5x^5y+0-6xy^3$

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

Therefore $3x^5y-2x^3y^4-7xy^3+(-8x^5y+2x^3y^4+xy^3)=-5x^5y-6xy^3$

In the simplified sum of the polynomials $-5x^5y-6xy^3$  we have the degree is 6

Now difference the polynomials

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

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

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

Therefore $3x^5y-2x^3y^4-7xy^3-(-8x^5y+2x^3y^4+xy^3)=11x^5y-4x^3y^4-8xy^3$

In the simplified difference of polynomials $11x^5y-4x^3y^4-8xy^3$ we have the degree is 7

Therefore the option " The sum has degree of 6 , but the difference has a degree of 7 " is correct