Answer :
Let's solve the algebraic subtraction step by step.
The expression given is:
[tex]\[
\left(-4x^4 + 8x^6 + 8 + 6x^5\right) - \left(-9 + 2x^5 + 6x^6 + 9x^4\right)
\][/tex]
First, distribute the negative sign to the terms in the second parenthesis:
[tex]\[
-4x^4 + 8x^6 + 8 + 6x^5 - (-9) - 2x^5 - 6x^6 - 9x^4
\][/tex]
Simplify by changing the sign of each term in the second polynomial:
[tex]\[
-4x^4 + 8x^6 + 8 + 6x^5 + 9 - 2x^5 - 6x^6 - 9x^4
\][/tex]
Next, let's combine like terms:
- Combine [tex]\(x^6\)[/tex] terms: [tex]\(8x^6 - 6x^6 = 2x^6\)[/tex]
- Combine [tex]\(x^5\)[/tex] terms: [tex]\(6x^5 - 2x^5 = 4x^5\)[/tex]
- Combine [tex]\(x^4\)[/tex] terms: [tex]\(-4x^4 - 9x^4 = -13x^4\)[/tex]
- Combine constant terms: [tex]\(8 + 9 = 17\)[/tex]
So, the resulting polynomial after subtracting the given polynomials is:
[tex]\[
2x^6 + 4x^5 - 13x^4 + 17
\][/tex]
The correct answer is:
[tex]\[ 2x^6 + 4x^5 - 13x^4 + 17 \][/tex]
This corresponds to the second choice:
[tex]\[ 2x^6 + 4x^5 - 13x^4 + 17 \][/tex]
The expression given is:
[tex]\[
\left(-4x^4 + 8x^6 + 8 + 6x^5\right) - \left(-9 + 2x^5 + 6x^6 + 9x^4\right)
\][/tex]
First, distribute the negative sign to the terms in the second parenthesis:
[tex]\[
-4x^4 + 8x^6 + 8 + 6x^5 - (-9) - 2x^5 - 6x^6 - 9x^4
\][/tex]
Simplify by changing the sign of each term in the second polynomial:
[tex]\[
-4x^4 + 8x^6 + 8 + 6x^5 + 9 - 2x^5 - 6x^6 - 9x^4
\][/tex]
Next, let's combine like terms:
- Combine [tex]\(x^6\)[/tex] terms: [tex]\(8x^6 - 6x^6 = 2x^6\)[/tex]
- Combine [tex]\(x^5\)[/tex] terms: [tex]\(6x^5 - 2x^5 = 4x^5\)[/tex]
- Combine [tex]\(x^4\)[/tex] terms: [tex]\(-4x^4 - 9x^4 = -13x^4\)[/tex]
- Combine constant terms: [tex]\(8 + 9 = 17\)[/tex]
So, the resulting polynomial after subtracting the given polynomials is:
[tex]\[
2x^6 + 4x^5 - 13x^4 + 17
\][/tex]
The correct answer is:
[tex]\[ 2x^6 + 4x^5 - 13x^4 + 17 \][/tex]
This corresponds to the second choice:
[tex]\[ 2x^6 + 4x^5 - 13x^4 + 17 \][/tex]
