Answer :
We start with the problem of finding the difference between the two expressions:
[tex]$$
\text{Expression 1: } x^3 - 6x^5 + 7x^4
$$[/tex]
[tex]$$
\text{Expression 2: } x^4 - 2x^3 + 7x^5
$$[/tex]
Since we need to subtract Expression 2 from Expression 1, we write:
[tex]$$
(x^3 - 6x^5 + 7x^4) - (x^4 - 2x^3 + 7x^5)
$$[/tex]
### Step 1: Distribute the Negative Sign
We distribute the negative sign to each term inside the second parenthesis:
[tex]$$
x^3 - 6x^5 + 7x^4 - x^4 + 2x^3 - 7x^5
$$[/tex]
### Step 2: Combine Like Terms
- For the [tex]\(x^5\)[/tex] terms:
[tex]\[
-6x^5 - 7x^5 = -13x^5
\][/tex]
- For the [tex]\(x^4\)[/tex] terms:
[tex]\[
7x^4 - x^4 = 6x^4
\][/tex]
- For the [tex]\(x^3\)[/tex] terms:
[tex]\[
x^3 + 2x^3 = 3x^3
\][/tex]
### Step 3: Write the Final Expression
Combining the results:
[tex]$$
-13x^5 + 6x^4 + 3x^3
$$[/tex]
Thus, the final answer is:
[tex]$$
\boxed{-13x^5 + 6x^4 + 3x^3}
$$[/tex]
This matches answer option D.
[tex]$$
\text{Expression 1: } x^3 - 6x^5 + 7x^4
$$[/tex]
[tex]$$
\text{Expression 2: } x^4 - 2x^3 + 7x^5
$$[/tex]
Since we need to subtract Expression 2 from Expression 1, we write:
[tex]$$
(x^3 - 6x^5 + 7x^4) - (x^4 - 2x^3 + 7x^5)
$$[/tex]
### Step 1: Distribute the Negative Sign
We distribute the negative sign to each term inside the second parenthesis:
[tex]$$
x^3 - 6x^5 + 7x^4 - x^4 + 2x^3 - 7x^5
$$[/tex]
### Step 2: Combine Like Terms
- For the [tex]\(x^5\)[/tex] terms:
[tex]\[
-6x^5 - 7x^5 = -13x^5
\][/tex]
- For the [tex]\(x^4\)[/tex] terms:
[tex]\[
7x^4 - x^4 = 6x^4
\][/tex]
- For the [tex]\(x^3\)[/tex] terms:
[tex]\[
x^3 + 2x^3 = 3x^3
\][/tex]
### Step 3: Write the Final Expression
Combining the results:
[tex]$$
-13x^5 + 6x^4 + 3x^3
$$[/tex]
Thus, the final answer is:
[tex]$$
\boxed{-13x^5 + 6x^4 + 3x^3}
$$[/tex]
This matches answer option D.
