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]
[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]
