Answer :
We start with the expression
[tex]$$
(7x + 2 + 8x^4) - (2x - 5 - 8x^4) + (3x + 5x^4).
$$[/tex]
Step 1: Distribute the Minus Sign
In the second group, distribute the negative sign:
[tex]$$
-(2x - 5 - 8x^4) = -2x + 5 + 8x^4.
$$[/tex]
Now the expression becomes:
[tex]$$
7x + 2 + 8x^4 - 2x + 5 + 8x^4 + 3x + 5x^4.
$$[/tex]
Step 2: Combine Like Terms
Group the like terms together.
1. [tex]$x^4$[/tex] Terms:
[tex]$$
8x^4 + 8x^4 + 5x^4 = 21x^4.
$$[/tex]
2. [tex]$x$[/tex] Terms:
[tex]$$
7x - 2x + 3x = 8x.
$$[/tex]
3. Constant Terms:
[tex]$$
2 + 5 = 7.
$$[/tex]
Step 3: Write the Simplified Expression
Putting it all together, we have:
[tex]$$
21x^4 + 8x + 7.
$$[/tex]
Thus, the simplified expression is
[tex]$$
\boxed{21x^4 + 8x + 7},
$$[/tex]
which corresponds to choice D.
[tex]$$
(7x + 2 + 8x^4) - (2x - 5 - 8x^4) + (3x + 5x^4).
$$[/tex]
Step 1: Distribute the Minus Sign
In the second group, distribute the negative sign:
[tex]$$
-(2x - 5 - 8x^4) = -2x + 5 + 8x^4.
$$[/tex]
Now the expression becomes:
[tex]$$
7x + 2 + 8x^4 - 2x + 5 + 8x^4 + 3x + 5x^4.
$$[/tex]
Step 2: Combine Like Terms
Group the like terms together.
1. [tex]$x^4$[/tex] Terms:
[tex]$$
8x^4 + 8x^4 + 5x^4 = 21x^4.
$$[/tex]
2. [tex]$x$[/tex] Terms:
[tex]$$
7x - 2x + 3x = 8x.
$$[/tex]
3. Constant Terms:
[tex]$$
2 + 5 = 7.
$$[/tex]
Step 3: Write the Simplified Expression
Putting it all together, we have:
[tex]$$
21x^4 + 8x + 7.
$$[/tex]
Thus, the simplified expression is
[tex]$$
\boxed{21x^4 + 8x + 7},
$$[/tex]
which corresponds to choice D.
