High School

Simplify the expression:

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

Choose the correct option:

A) [tex]15x^4 + 19x + 7[/tex]
B) [tex]21x^4 + 14x + 7[/tex]
C) [tex]21x^4 + 8x + 7[/tex]
D) [tex]15x^4 + 14x + 7[/tex]

Answer :

Let's simplify the given expression step by step:

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

1. Remove the parentheses:
- When removing the second set of parentheses, distribute the negative sign:
[tex]\((7x + 2 + 8x^4) - 2x + 5 + 8x^4 + (3x + 5x^4)\)[/tex].

2. Combine like terms:
- For [tex]\(x^4\)[/tex] terms:
- First set: [tex]\(+8x^4\)[/tex]
- Second set: [tex]\(+8x^4\)[/tex] after distributing the negative sign
- Third set: [tex]\(+5x^4\)[/tex]
- Total for [tex]\(x^4\)[/tex] terms: [tex]\(8x^4 + 8x^4 + 5x^4 = 21x^4\)[/tex].

- For [tex]\(x\)[/tex] terms:
- First set: [tex]\(+7x\)[/tex]
- Second set: [tex]\(-2x\)[/tex]
- Third set: [tex]\(+3x\)[/tex]
- Total for [tex]\(x\)[/tex] terms: [tex]\(7x - 2x + 3x = 8x\)[/tex].

- For constant terms:
- First set: [tex]\(+2\)[/tex]
- From the simplified second set: [tex]\(+5\)[/tex]
- Total constant: [tex]\(2 + 5 = 7\)[/tex].

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

Therefore, the correct answer is:
C) [tex]\(21x^4 + 8x + 7\)[/tex].

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