Answer :
To solve the problem, we need to simplify the expression by combining like terms and then write it in descending order of powers of [tex]\( x \)[/tex].
Given expression:
[tex]\[
\left(6x^5 + 3x^7 - 5 - 9x^6\right) - \left(-3 - 2x^6 + 7x^7 + 4x^5\right)
\][/tex]
First, eliminate the parentheses by distributing the negative sign through the second expression:
[tex]\[
6x^5 + 3x^7 - 5 - 9x^6 - (-3) - (-2x^6) - (7x^7) - (4x^5)
\][/tex]
Simplify the expression:
[tex]\[
6x^5 + 3x^7 - 5 - 9x^6 + 3 + 2x^6 - 7x^7 - 4x^5
\][/tex]
Next, combine like terms:
Combine the [tex]\(x^7\)[/tex] terms:
[tex]\[
3x^7 - 7x^7 = -4x^7
\][/tex]
Combine the [tex]\(x^6\)[/tex] terms:
[tex]\[
-9x^6 + 2x^6 = -7x^6
\][/tex]
Combine the [tex]\(x^5\)[/tex] terms:
[tex]\[
6x^5 - 4x^5 = 2x^5
\][/tex]
Combine the constant terms:
[tex]\[
-5 + 3 = -2
\][/tex]
Now, write the combined terms in a single expression in descending order of powers of [tex]\( x \)[/tex]:
[tex]\[
-4x^7 - 7x^6 + 2x^5 - 2
\][/tex]
So the simplified expression, in descending order, is:
[tex]\[
\boxed{-4x^7 - 7x^6 + 2x^5 - 2}
\][/tex]
Given expression:
[tex]\[
\left(6x^5 + 3x^7 - 5 - 9x^6\right) - \left(-3 - 2x^6 + 7x^7 + 4x^5\right)
\][/tex]
First, eliminate the parentheses by distributing the negative sign through the second expression:
[tex]\[
6x^5 + 3x^7 - 5 - 9x^6 - (-3) - (-2x^6) - (7x^7) - (4x^5)
\][/tex]
Simplify the expression:
[tex]\[
6x^5 + 3x^7 - 5 - 9x^6 + 3 + 2x^6 - 7x^7 - 4x^5
\][/tex]
Next, combine like terms:
Combine the [tex]\(x^7\)[/tex] terms:
[tex]\[
3x^7 - 7x^7 = -4x^7
\][/tex]
Combine the [tex]\(x^6\)[/tex] terms:
[tex]\[
-9x^6 + 2x^6 = -7x^6
\][/tex]
Combine the [tex]\(x^5\)[/tex] terms:
[tex]\[
6x^5 - 4x^5 = 2x^5
\][/tex]
Combine the constant terms:
[tex]\[
-5 + 3 = -2
\][/tex]
Now, write the combined terms in a single expression in descending order of powers of [tex]\( x \)[/tex]:
[tex]\[
-4x^7 - 7x^6 + 2x^5 - 2
\][/tex]
So the simplified expression, in descending order, is:
[tex]\[
\boxed{-4x^7 - 7x^6 + 2x^5 - 2}
\][/tex]
