Answer :
We are given the expression
[tex]$$
\left(3x^4 + 2 - 2x^3\right) + \left(4x^3 + 4x^4\right).
$$[/tex]
Step 1. Remove the parentheses
Since the expression is a sum, we can drop the parentheses:
[tex]$$
3x^4 + 2 - 2x^3 + 4x^3 + 4x^4.
$$[/tex]
Step 2. Combine like terms
Group the terms with the same powers of [tex]$x$[/tex]:
- For the [tex]$x^4$[/tex] terms:
[tex]$$
3x^4 + 4x^4 = 7x^4.
$$[/tex]
- For the [tex]$x^3$[/tex] terms:
[tex]$$
-2x^3 + 4x^3 = 2x^3.
$$[/tex]
- The constant term remains:
[tex]$$
2.
$$[/tex]
Step 3. Write the simplified expression
After combining like terms, the simplified expression is:
[tex]$$
7x^4 + 2x^3 + 2.
$$[/tex]
This matches option A:
[tex]$$
7x^4+2x^3+2.
$$[/tex]
Thus, the answer is [tex]$\boxed{7 x^4+2 x^3+2}$[/tex].
[tex]$$
\left(3x^4 + 2 - 2x^3\right) + \left(4x^3 + 4x^4\right).
$$[/tex]
Step 1. Remove the parentheses
Since the expression is a sum, we can drop the parentheses:
[tex]$$
3x^4 + 2 - 2x^3 + 4x^3 + 4x^4.
$$[/tex]
Step 2. Combine like terms
Group the terms with the same powers of [tex]$x$[/tex]:
- For the [tex]$x^4$[/tex] terms:
[tex]$$
3x^4 + 4x^4 = 7x^4.
$$[/tex]
- For the [tex]$x^3$[/tex] terms:
[tex]$$
-2x^3 + 4x^3 = 2x^3.
$$[/tex]
- The constant term remains:
[tex]$$
2.
$$[/tex]
Step 3. Write the simplified expression
After combining like terms, the simplified expression is:
[tex]$$
7x^4 + 2x^3 + 2.
$$[/tex]
This matches option A:
[tex]$$
7x^4+2x^3+2.
$$[/tex]
Thus, the answer is [tex]$\boxed{7 x^4+2 x^3+2}$[/tex].
