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Answer :
Let's solve the algebraic expression step-by-step:
We have the algebraic subtraction:
[tex]\[
(-4x^4 + 8x^6 + 8 + 6x^5) - (-9 + 2x^5 + 6x^6 + 9x^4)
\][/tex]
The first step in solving this is to distribute the negative sign across the second expression. This means we change the signs of each term in the second expression:
[tex]\[
- (-9) = +9
\][/tex]
[tex]\[
- (2x^5) = -2x^5
\][/tex]
[tex]\[
- (6x^6) = -6x^6
\][/tex]
[tex]\[
- (9x^4) = -9x^4
\][/tex]
Now, rewrite the subtraction as an addition with these new terms:
[tex]\[
-4x^4 + 8x^6 + 8 + 6x^5 + 9 - 2x^5 - 6x^6 - 9x^4
\][/tex]
Next, we combine like terms:
- Combine the [tex]\(x^6\)[/tex] terms: [tex]\(8x^6 - 6x^6 = 2x^6\)[/tex]
- Combine the [tex]\(x^5\)[/tex] terms: [tex]\(6x^5 - 2x^5 = 4x^5\)[/tex]
- Combine the [tex]\(x^4\)[/tex] terms: [tex]\(-4x^4 - 9x^4 = -13x^4\)[/tex]
- Combine the constant terms: [tex]\(8 + 9 = 17\)[/tex]
Putting it all together, the simplified expression is:
[tex]\[
2x^6 + 4x^5 - 13x^4 + 17
\][/tex]
Therefore, the correct answer is:
[tex]\(2x^6 + 4x^5 - 13x^4 + 17\)[/tex]
This matches the option [tex]\[
2x^6 + 4x^5 - 13x^4 + 17
\][/tex]
We have the algebraic subtraction:
[tex]\[
(-4x^4 + 8x^6 + 8 + 6x^5) - (-9 + 2x^5 + 6x^6 + 9x^4)
\][/tex]
The first step in solving this is to distribute the negative sign across the second expression. This means we change the signs of each term in the second expression:
[tex]\[
- (-9) = +9
\][/tex]
[tex]\[
- (2x^5) = -2x^5
\][/tex]
[tex]\[
- (6x^6) = -6x^6
\][/tex]
[tex]\[
- (9x^4) = -9x^4
\][/tex]
Now, rewrite the subtraction as an addition with these new terms:
[tex]\[
-4x^4 + 8x^6 + 8 + 6x^5 + 9 - 2x^5 - 6x^6 - 9x^4
\][/tex]
Next, we combine like terms:
- Combine the [tex]\(x^6\)[/tex] terms: [tex]\(8x^6 - 6x^6 = 2x^6\)[/tex]
- Combine the [tex]\(x^5\)[/tex] terms: [tex]\(6x^5 - 2x^5 = 4x^5\)[/tex]
- Combine the [tex]\(x^4\)[/tex] terms: [tex]\(-4x^4 - 9x^4 = -13x^4\)[/tex]
- Combine the constant terms: [tex]\(8 + 9 = 17\)[/tex]
Putting it all together, the simplified expression is:
[tex]\[
2x^6 + 4x^5 - 13x^4 + 17
\][/tex]
Therefore, the correct answer is:
[tex]\(2x^6 + 4x^5 - 13x^4 + 17\)[/tex]
This matches the option [tex]\[
2x^6 + 4x^5 - 13x^4 + 17
\][/tex]
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