Question

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

Answer 1

8r^6s^3 - 9r^5s^4 + 3r^4s^5 - (2r^4s^5 - 5r^3s^6 - 4r^5s^4) =
8r^6s^3 - 9r^5s^4 + 3r^4s^5 - 2r^4s^5 + 5r^3s^6 + 4r^5s^4 =
8r^6s^3 -5r^5s^4 + r^4s^5 + 5r^3s^6 <==

Answer 2

Answer:  The required difference is $8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.$

Step-by-step explanation:  We are given to find the difference of the polynomials as follows :

$DP=(8r^6s^3-9r^5s^4+3r^4s^5)-(2r^4s^5-5r^3s^6-4r^5s^4)~~~~~~~~~~~~~~~~~~~(i)$

To find the given difference, we need to choose the terms with same poers of the unknown variables r and s and then subtract their coefficients.

The difference (i) is as follows :

$DP\\\\=(8r^6s^3-9r^5s^4+3r^4s^5)-(2r^4s^5-5r^3s^6-4r^5s^4)\\\\=8r^6s^3-9r^5s^4+3r^4s^5-2r^4s^5+5r^3s^6+4r^5s^4\\\\=8r^6s^3+(4-9)r^5s^4+(3-2)r^4s^5+5r^3s^6\\\\=8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.$

Thus, the required difference is $8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.$