What is the difference of the polynomials? (8r6s3 – 9r5s4 3r4s5) – (2r4s5 – 5r3s6 – 4r5s4)

To answer the question above, distribute the negative sign to the subtrahend and combine like terms.
8r6s3 - 9r5s4 + 3r4s5 - 2r4s5 + 5r3s6 + 4r5s4
Combining like terms
8r6s3 + (-9r5s4 + 4r5s4) + (3r4s5 - 2r4s5) + 5r3s6

Simplifying the expressions will give an answer of,

8r6s3 - 5r5s4 + r4s5 + 5r3s6

Answer Link

MrRoyal MrRoyal · Answer 2 · 2022-05-18T11:05:09+02:00

The difference of the polynomials [tex](8r^6s^3 - 9r^5s^4 + 3r^4s^5) - (2r^4s^5 - 5r^3s^6 - 4r^5s^4)[/tex] is [tex]8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6[/tex]

How to determine the difference?

The expression is given as:

[tex](8r^6s^3 - 9r^5s^4 + 3r^4s^5) - (2r^4s^5 - 5r^3s^6 - 4r^5s^4)[/tex]

Open the bracket

[tex]8r^6s^3 - 9r^5s^4 + 3r^4s^5 - 2r^4s^5 + 5r^3s^6 + 4r^5s^4[/tex]

Collect like terms

[tex]8r^6s^3 - 9r^5s^4 + 4r^5s^4 + 3r^4s^5 - 2r^4s^5 + 5r^3s^6[/tex]

Evaluate the like terms

[tex]8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6[/tex]

Hence, the difference of the polynomials [tex](8r^6s^3 - 9r^5s^4 + 3r^4s^5) - (2r^4s^5 - 5r^3s^6 - 4r^5s^4)[/tex] is [tex]8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6[/tex]