Answer :
We need to simplify the expression
[tex]$$
\left(6 x^5-3 x^4-3 x\right)+\left(5 x^5+8 x^4+8 x\right).
$$[/tex]
### Step 1. Group Like Terms
Group the terms with the same power of [tex]$x$[/tex]:
- For [tex]$x^5$[/tex]: [tex]$$6x^5 + 5x^5$$[/tex]
- For [tex]$x^4$[/tex]: [tex]$$-3x^4 + 8x^4$$[/tex]
- For [tex]$x$[/tex]: [tex]$$-3x + 8x$$[/tex]
### Step 2. Combine the Terms
Now, add the coefficients for each group:
- [tex]$x^5$[/tex] terms:
[tex]$$
6x^5 + 5x^5 = 11x^5
$$[/tex]
- [tex]$x^4$[/tex] terms:
[tex]$$
-3x^4 + 8x^4 = 5x^4
$$[/tex]
- [tex]$x$[/tex] terms:
[tex]$$
-3x + 8x = 5x
$$[/tex]
### Step 3. Write the Final Answer
After combining all like terms, the simplified expression is:
[tex]$$
11x^5 + 5x^4 + 5x.
$$[/tex]
Thus, the correct answer is:
[tex]$$
11 x^5+5 x^4+5 x.
$$[/tex]
[tex]$$
\left(6 x^5-3 x^4-3 x\right)+\left(5 x^5+8 x^4+8 x\right).
$$[/tex]
### Step 1. Group Like Terms
Group the terms with the same power of [tex]$x$[/tex]:
- For [tex]$x^5$[/tex]: [tex]$$6x^5 + 5x^5$$[/tex]
- For [tex]$x^4$[/tex]: [tex]$$-3x^4 + 8x^4$$[/tex]
- For [tex]$x$[/tex]: [tex]$$-3x + 8x$$[/tex]
### Step 2. Combine the Terms
Now, add the coefficients for each group:
- [tex]$x^5$[/tex] terms:
[tex]$$
6x^5 + 5x^5 = 11x^5
$$[/tex]
- [tex]$x^4$[/tex] terms:
[tex]$$
-3x^4 + 8x^4 = 5x^4
$$[/tex]
- [tex]$x$[/tex] terms:
[tex]$$
-3x + 8x = 5x
$$[/tex]
### Step 3. Write the Final Answer
After combining all like terms, the simplified expression is:
[tex]$$
11x^5 + 5x^4 + 5x.
$$[/tex]
Thus, the correct answer is:
[tex]$$
11 x^5+5 x^4+5 x.
$$[/tex]
