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Answer :
We start with the expression
[tex]$$
\left(7x+2+8x^4\right)-\left(2x-5-8x^4\right)+\left(3x+5x^4\right).
$$[/tex]
Step 1. Remove Parentheses
In the second term, distribute the minus sign:
[tex]$$
-\left(2x-5-8x^4\right) = -2x + 5 + 8x^4.
$$[/tex]
Thus, the expression becomes:
[tex]\[
7x + 2 + 8x^4 -2x + 5 + 8x^4 + 3x + 5x^4.
\][/tex]
Step 2. Group Like Terms
Group the terms with the same power of [tex]$x$[/tex]:
- For [tex]$x^4$[/tex] terms:
[tex]$$
8x^4 + 8x^4 + 5x^4 = (8+8+5)x^4 = 21x^4.
$$[/tex]
- For [tex]$x$[/tex] terms:
[tex]$$
7x - 2x + 3x = (7-2+3)x = 8x.
$$[/tex]
- For constant terms:
[tex]$$
2 + 5 = 7.
$$[/tex]
Step 3. Write the Final Simplified Expression
Combining the results, we have:
[tex]$$
21x^4 + 8x + 7.
$$[/tex]
This corresponds to option A.
[tex]$$
\left(7x+2+8x^4\right)-\left(2x-5-8x^4\right)+\left(3x+5x^4\right).
$$[/tex]
Step 1. Remove Parentheses
In the second term, distribute the minus sign:
[tex]$$
-\left(2x-5-8x^4\right) = -2x + 5 + 8x^4.
$$[/tex]
Thus, the expression becomes:
[tex]\[
7x + 2 + 8x^4 -2x + 5 + 8x^4 + 3x + 5x^4.
\][/tex]
Step 2. Group Like Terms
Group the terms with the same power of [tex]$x$[/tex]:
- For [tex]$x^4$[/tex] terms:
[tex]$$
8x^4 + 8x^4 + 5x^4 = (8+8+5)x^4 = 21x^4.
$$[/tex]
- For [tex]$x$[/tex] terms:
[tex]$$
7x - 2x + 3x = (7-2+3)x = 8x.
$$[/tex]
- For constant terms:
[tex]$$
2 + 5 = 7.
$$[/tex]
Step 3. Write the Final Simplified Expression
Combining the results, we have:
[tex]$$
21x^4 + 8x + 7.
$$[/tex]
This corresponds to option A.
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