Answer :
To simplify the expression [tex]\((3x^2 + 4) + (6x^2 - 4x - 6)\)[/tex], let's combine like terms step-by-step:
1. Identify and combine the like terms:
- [tex]\(x^2\)[/tex] terms: Combine [tex]\(3x^2\)[/tex] from the first expression with [tex]\(6x^2\)[/tex] from the second expression.
[tex]\[
3x^2 + 6x^2 = 9x^2
\][/tex]
- [tex]\(x\)[/tex] terms: There is only one [tex]\(x\)[/tex] term, [tex]\(-4x\)[/tex], which comes from the second expression. Since there is no other [tex]\(x\)[/tex] term to combine it with, it remains the same.
- Constant terms: Combine [tex]\(4\)[/tex] from the first expression with [tex]\(-6\)[/tex] from the second expression.
[tex]\[
4 + (-6) = -2
\][/tex]
2. Write the simplified expression:
After combining all the like terms, we get the simplified expression:
[tex]\[
9x^2 - 4x - 2
\][/tex]
Therefore, the correct choice from the given options is d) [tex]\(9x^2 - 4x - 2\)[/tex].
1. Identify and combine the like terms:
- [tex]\(x^2\)[/tex] terms: Combine [tex]\(3x^2\)[/tex] from the first expression with [tex]\(6x^2\)[/tex] from the second expression.
[tex]\[
3x^2 + 6x^2 = 9x^2
\][/tex]
- [tex]\(x\)[/tex] terms: There is only one [tex]\(x\)[/tex] term, [tex]\(-4x\)[/tex], which comes from the second expression. Since there is no other [tex]\(x\)[/tex] term to combine it with, it remains the same.
- Constant terms: Combine [tex]\(4\)[/tex] from the first expression with [tex]\(-6\)[/tex] from the second expression.
[tex]\[
4 + (-6) = -2
\][/tex]
2. Write the simplified expression:
After combining all the like terms, we get the simplified expression:
[tex]\[
9x^2 - 4x - 2
\][/tex]
Therefore, the correct choice from the given options is d) [tex]\(9x^2 - 4x - 2\)[/tex].
