rasasweat rasasweat

05-01-2020
Mathematics

contestada

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.

Respuesta :

jchoubay1 jchoubay1

14-02-2020

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 [tex]3x^5y-2x^3y^4-7xy^3[/tex] and [tex]-8x^5y+2x^3y^4+xy^3[/tex]

Now sum the given 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+0-6xy^3[/tex]

[tex]=-5x^5y-6xy^3[/tex]

Therefore [tex]3x^5y-2x^3y^4-7xy^3+(-8x^5y+2x^3y^4+xy^3)=-5x^5y-6xy^3[/tex]

In the simplified sum of the polynomials [tex]-5x^5y-6xy^3[/tex] we have the degree is 6

Now difference the 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]=11x^5y-4x^3y^4-8xy^3[/tex]

Therefore [tex]3x^5y-2x^3y^4-7xy^3-(-8x^5y+2x^3y^4+xy^3)=11x^5y-4x^3y^4-8xy^3[/tex]

In the simplified difference of polynomials [tex]11x^5y-4x^3y^4-8xy^3[/tex] 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

Answer Link

bellaelithebethchild bellaelithebethchild

21-02-2020

Answer:

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

Step-by-step explanation:

Answer Link

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