Answer :
To solve the given problem, we need to combine and simplify two polynomial expressions:
1. Given Expressions:
- The first expression is: [tex]\(-7x^2 - 3x^4 - 5\)[/tex]
- The second expression is: [tex]\(-3x^4 + 9x^2 + 3\)[/tex]
2. Combine the Expressions:
- Start by combining the like terms from both expressions.
3. Simplify Step-by-step:
- Combine the [tex]\(x^4\)[/tex] terms:
- From the first expression, the [tex]\(x^4\)[/tex] term is [tex]\(-3x^4\)[/tex].
- From the second expression, the [tex]\(x^4\)[/tex] term is [tex]\(-3x^4\)[/tex].
- Combine: [tex]\(-3x^4 + (-3x^4) = -6x^4\)[/tex].
- Combine the [tex]\(x^2\)[/tex] terms:
- From the first expression, the [tex]\(x^2\)[/tex] term is [tex]\(-7x^2\)[/tex].
- From the second expression, the [tex]\(x^2\)[/tex] term is [tex]\(9x^2\)[/tex].
- Combine: [tex]\(-7x^2 + 9x^2 = 2x^2\)[/tex].
- Combine the constant terms:
- The constant term from the first expression is [tex]\(-5\)[/tex].
- The constant term from the second expression is [tex]\(3\)[/tex].
- Combine: [tex]\(-5 + 3 = -2\)[/tex].
4. Final Simplified Expression:
- Bringing it all together, we have:
[tex]\[
-6x^4 + 2x^2 - 2
\][/tex]
This step-by-step combination and simplification result in the expression [tex]\(-6x^4 + 2x^2 - 2\)[/tex], which matches option [A] from the given choices.
1. Given Expressions:
- The first expression is: [tex]\(-7x^2 - 3x^4 - 5\)[/tex]
- The second expression is: [tex]\(-3x^4 + 9x^2 + 3\)[/tex]
2. Combine the Expressions:
- Start by combining the like terms from both expressions.
3. Simplify Step-by-step:
- Combine the [tex]\(x^4\)[/tex] terms:
- From the first expression, the [tex]\(x^4\)[/tex] term is [tex]\(-3x^4\)[/tex].
- From the second expression, the [tex]\(x^4\)[/tex] term is [tex]\(-3x^4\)[/tex].
- Combine: [tex]\(-3x^4 + (-3x^4) = -6x^4\)[/tex].
- Combine the [tex]\(x^2\)[/tex] terms:
- From the first expression, the [tex]\(x^2\)[/tex] term is [tex]\(-7x^2\)[/tex].
- From the second expression, the [tex]\(x^2\)[/tex] term is [tex]\(9x^2\)[/tex].
- Combine: [tex]\(-7x^2 + 9x^2 = 2x^2\)[/tex].
- Combine the constant terms:
- The constant term from the first expression is [tex]\(-5\)[/tex].
- The constant term from the second expression is [tex]\(3\)[/tex].
- Combine: [tex]\(-5 + 3 = -2\)[/tex].
4. Final Simplified Expression:
- Bringing it all together, we have:
[tex]\[
-6x^4 + 2x^2 - 2
\][/tex]
This step-by-step combination and simplification result in the expression [tex]\(-6x^4 + 2x^2 - 2\)[/tex], which matches option [A] from the given choices.
