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

Explanation:

Answer 2

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

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