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Simplify [tex]\left(7x + 2 + 8x^4\right) - \left(2x - 5 - 8x^4\right) + \left(3x + 5x^4\right)[/tex].

A) [tex]21x^4 + 8x + 7[/tex]

B) [tex]15x^4 + 14x + 7[/tex]

C) [tex]21x^4 + 14x + 7[/tex]

D) [tex]15x^4 + 19x + 7[/tex]

Answer :

Let's simplify the given expression step-by-step:

[tex]\[
(7x + 2 + 8x^4) - (2x - 5 - 8x^4) + (3x + 5x^4)
\][/tex]

First, we need to remove the parentheses by distributing any negative signs:

1. The first part remains the same:
[tex]\[
7x + 2 + 8x^4
\][/tex]

2. For the second part, distribute the negative sign through the parentheses:
[tex]\[
-(2x - 5 - 8x^4) = -2x + 5 + 8x^4
\][/tex]

3. The third part remains the same:
[tex]\[
3x + 5x^4
\][/tex]

Now, combine all parts together:
[tex]\[
(7x + 2 + 8x^4) + (-2x + 5 + 8x^4) + (3x + 5x^4)
\][/tex]

Next, group the like terms:

- Combine the [tex]\( x^4 \)[/tex] terms:
[tex]\[
8x^4 + 8x^4 + 5x^4 = 21x^4
\][/tex]

- Combine the [tex]\( x \)[/tex] terms:
[tex]\[
7x - 2x + 3x = 8x
\][/tex]

- Combine the constant terms:
[tex]\[
2 + 5 = 7
\][/tex]

Putting it all together, the simplified expression is:
[tex]\[
21x^4 + 8x + 7
\][/tex]

So, the correct answer is:

[tex]\[
\boxed{21x^4 + 8x + 7}
\][/tex]

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