To determine which expression is equivalent to the given expression [tex]\(3x^2 + 5x - 7(x^2 + 4)\)[/tex], we can follow these steps to simplify it:
1. Distribute the [tex]\(-7\)[/tex] within the parentheses:
[tex]\[
-7(x^2 + 4) = -7x^2 - 28
\][/tex]
2. Rewrite the original expression with the distribution applied:
[tex]\[
3x^2 + 5x - 7x^2 - 28
\][/tex]
3. Combine like terms:
- First, combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
3x^2 - 7x^2 = -4x^2
\][/tex]
- Then, combine the constants and the [tex]\(x\)[/tex] term:
[tex]\[
-4x^2 + 5x - 28
\][/tex]
So, the simplified form of the expression [tex]\(3x^2 + 5x - 7(x^2 + 4)\)[/tex] is:
[tex]\[
-4x^2 + 5x - 28
\][/tex]
Now, let's compare this simplified expression with the given options:
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]
We see that our simplified expression [tex]\(-4x^2 + 5x - 28\)[/tex] matches option B exactly.
Therefore, the expression that is equivalent to [tex]\(3x^2 + 5x - 7(x^2 + 4)\)[/tex] is option B: [tex]\(-4x^2 + 5x - 28\)[/tex].
