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What is the difference of the polynomials?

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

A. [tex]\(6r^6s^3 - 4r^5s^4 + 7r^4s^5\)[/tex]

B. [tex]\(6r^6s^3 - 13r^5s^4 - r^4s^5\)[/tex]

C. [tex]\(8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6\)[/tex]

D. [tex]\(8r^6s^3 - 13r^5s^4 + r^4s^5 - 5r^3s^6\)[/tex]

Sagot :

GinnyAnsweridn
To find the difference of the given polynomials, we need to perform polynomial subtraction step by step.

Given polynomials:
[tex]\[ P_1 = 8r^6s^3 - 9r^5s^4 + 3r^4s^5 \][/tex]
[tex]\[ P_2 = 2r^4s^5 - 5r^3s^6 - 4r^5s^4 \][/tex]

We are asked to find:
[tex]\[ P_1 - P_2 = (8r^6s^3 - 9r^5s^4 + 3r^4s^5) - (2r^4s^5 - 5r^3s^6 - 4r^5s^4) \][/tex]

First, let's distribute the negative sign through [tex]\( P_2 \)[/tex]:
[tex]\[ P_1 - P_2 = 8r^6s^3 - 9r^5s^4 + 3r^4s^5 - 2r^4s^5 + 5r^3s^6 + 4r^5s^4 \][/tex]

Next, we combine like terms:
1. Terms with [tex]\( r^6s^3 \)[/tex]:
[tex]\[ 8r^6s^3 \][/tex]

2. Terms with [tex]\( r^5s^4 \)[/tex]:
[tex]\[ -9r^5s^4 + 4r^5s^4 = -5r^5s^4 \][/tex]

3. Terms with [tex]\( r^4s^5 \)[/tex]:
[tex]\[ 3r^4s^5 - 2r^4s^5 = r^4s^5 \][/tex]

4. Terms with [tex]\( r^3s^6 \)[/tex]:
[tex]\[ 5r^3s^6 \][/tex]

Therefore, the difference of the polynomials is:
[tex]\[ 8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6 \][/tex]

Matching this with the given options, we find that the correct answer is:
[tex]\[ \boxed{8 r^6 s^3 - 5 r^5 s^4 + r^4 s^5 + 5 r^3 s^6} \][/tex]
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