Answer :
To solve the expression [tex]\((8x^3 + 8) - (x^3 - 2)\)[/tex], follow these steps:
1. Distribute the negative sign across the terms in the second expression:
The expression [tex]\((8x^3 + 8) - (x^3 - 2)\)[/tex] can be rewritten by distributing the negative sign:
[tex]\[
(8x^3 + 8) - x^3 + 2
\][/tex]
2. Combine like terms:
- For the [tex]\(x^3\)[/tex] terms:
[tex]\(8x^3 - x^3 = 7x^3\)[/tex]
- For the constant terms (numbers):
[tex]\(8 + 2 = 10\)[/tex]
3. Write the final simplified expression:
After combining the like terms, you have:
[tex]\[
7x^3 + 10
\][/tex]
Thus, the expression equivalent to [tex]\((8x^3 + 8) - (x^3 - 2)\)[/tex] is [tex]\(7x^3 + 10\)[/tex].
The correct choice is B) [tex]\(7x^3 + 10\)[/tex].
1. Distribute the negative sign across the terms in the second expression:
The expression [tex]\((8x^3 + 8) - (x^3 - 2)\)[/tex] can be rewritten by distributing the negative sign:
[tex]\[
(8x^3 + 8) - x^3 + 2
\][/tex]
2. Combine like terms:
- For the [tex]\(x^3\)[/tex] terms:
[tex]\(8x^3 - x^3 = 7x^3\)[/tex]
- For the constant terms (numbers):
[tex]\(8 + 2 = 10\)[/tex]
3. Write the final simplified expression:
After combining the like terms, you have:
[tex]\[
7x^3 + 10
\][/tex]
Thus, the expression equivalent to [tex]\((8x^3 + 8) - (x^3 - 2)\)[/tex] is [tex]\(7x^3 + 10\)[/tex].
The correct choice is B) [tex]\(7x^3 + 10\)[/tex].
