Select the correct answer.

Which expression is equivalent to the given expression?

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

A. [tex]\[ x^2 + 4 \][/tex]

B. [tex]\[ x^2 + 28 \][/tex]

C. [tex]\[ -4x^2 + 5x - 28 \][/tex]

D. [tex]\[ -4x^2 + 5x - 4 \][/tex]



Answer :

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]