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Answer :
We start with the expression
[tex]$$
(7x + 2 + 8x^4) - (2x - 5 - 8x^4) + (3x + 5x^4).
$$[/tex]
Step 1. Distribute the negative sign:
When subtracting the second group, we change the sign of each term inside the parentheses:
[tex]$$
(7x + 2 + 8x^4) - 2x + 5 + 8x^4 + (3x + 5x^4).
$$[/tex]
Step 2. Remove the parentheses:
Rewrite the expression without the parentheses:
[tex]$$
7x + 2 + 8x^4 - 2x + 5 + 8x^4 + 3x + 5x^4.
$$[/tex]
Step 3. Combine like terms:
- Group the [tex]$x^4$[/tex] terms:
[tex]$$8x^4 + 8x^4 + 5x^4 = 21x^4.$$[/tex]
- Group the [tex]$x$[/tex] terms:
[tex]$$7x - 2x + 3x = 8x.$$[/tex]
- Group the constant terms:
[tex]$$2 + 5 = 7.$$[/tex]
Step 4. Write the simplified expression:
Thus, the simplified expression is
[tex]$$
21x^4 + 8x + 7.
$$[/tex]
The answer is option B.
[tex]$$
(7x + 2 + 8x^4) - (2x - 5 - 8x^4) + (3x + 5x^4).
$$[/tex]
Step 1. Distribute the negative sign:
When subtracting the second group, we change the sign of each term inside the parentheses:
[tex]$$
(7x + 2 + 8x^4) - 2x + 5 + 8x^4 + (3x + 5x^4).
$$[/tex]
Step 2. Remove the parentheses:
Rewrite the expression without the parentheses:
[tex]$$
7x + 2 + 8x^4 - 2x + 5 + 8x^4 + 3x + 5x^4.
$$[/tex]
Step 3. Combine like terms:
- Group the [tex]$x^4$[/tex] terms:
[tex]$$8x^4 + 8x^4 + 5x^4 = 21x^4.$$[/tex]
- Group the [tex]$x$[/tex] terms:
[tex]$$7x - 2x + 3x = 8x.$$[/tex]
- Group the constant terms:
[tex]$$2 + 5 = 7.$$[/tex]
Step 4. Write the simplified expression:
Thus, the simplified expression is
[tex]$$
21x^4 + 8x + 7.
$$[/tex]
The answer is option B.
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