To determine which expression is equivalent to the given expression [tex]\( 3x^2 + 5x - 7(x^2 + 4) \)[/tex], follow these steps:
1. Distribute [tex]\(-7\)[/tex] across the terms inside the parentheses:
- Apply the distributive property to [tex]\(-7(x^2 + 4)\)[/tex]:
[tex]\[
-7(x^2 + 4) = -7x^2 - 28
\][/tex]
2. Rewrite the original expression with the distributed terms:
- Replace [tex]\(-7(x^2 + 4)\)[/tex] with [tex]\(-7x^2 - 28\)[/tex]:
[tex]\[
3x^2 + 5x - 7x^2 - 28
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(3x^2\)[/tex] and [tex]\(-7x^2\)[/tex]:
[tex]\[
3x^2 - 7x^2 = -4x^2
\][/tex]
- The remaining terms are [tex]\(5x\)[/tex] and [tex]\(-28\)[/tex]:
[tex]\[
-4x^2 + 5x - 28
\][/tex]
4. Identify the equivalent expression:
- The final simplified expression is:
[tex]\[
-4x^2 + 5x - 28
\][/tex]
Therefore, the correct answer is:
C. [tex]\(-4x^2 + 5x - 28\)[/tex]
