To find which expression is equivalent to the given expression:
[tex]\[ 3x^2 + 5x - 7(x^2 + 4) \][/tex]
Let's break it down step-by-step:
1. Expand the expression inside the parentheses:
[tex]\[ -7(x^2 + 4) \][/tex]
This will distribute [tex]\(-7\)[/tex] to both [tex]\(x^2\)[/tex] and [tex]\(4\)[/tex]:
[tex]\[ -7 \cdot x^2 - 7 \cdot 4 = -7x^2 - 28 \][/tex]
2. Combine the expanded expression with the other terms:
We now need to combine [tex]\(3x^2 + 5x\)[/tex] with [tex]\(-7x^2 - 28\)[/tex]:
[tex]\[ 3x^2 + 5x - 7x^2 - 28 \][/tex]
3. Simplify the combined expression:
Let's combine like terms:
[tex]\[ (3x^2 - 7x^2) + 5x - 28 \][/tex]
[tex]\[ -4x^2 + 5x - 28 \][/tex]
So, the simplified expression is:
[tex]\[ -4x^2 + 5x - 28 \][/tex]
Looking at the options provided:
A. [tex]\(x^2 + 28\)[/tex]
B. [tex]\(-4x^2 + 5x - 28\)[/tex]
C. [tex]\(-4x^2 + 5x - 4\)[/tex]
D. [tex]\(x^2 + 4\)[/tex]
The correct answer is:
B. [tex]\(-4x^2 + 5x - 28\)[/tex]
