To find which expression is equivalent to the given expression [tex]\(-2x^2 + 8x - 9 + 4x + 7x^2 + 2\)[/tex], we need to simplify it step by step by combining like terms.
1. Identify and combine the [tex]\(x^2\)[/tex] terms:
- The given expression has two [tex]\(x^2\)[/tex] terms: [tex]\(-2x^2\)[/tex] and [tex]\(7x^2\)[/tex].
- Combine these terms: [tex]\(-2x^2 + 7x^2 = 5x^2\)[/tex].
2. Identify and combine the [tex]\(x\)[/tex] terms:
- The given expression has two [tex]\(x\)[/tex] terms: [tex]\(8x\)[/tex] and [tex]\(4x\)[/tex].
- Combine these terms: [tex]\(8x + 4x = 12x\)[/tex].
3. Identify and combine the constant terms:
- The given expression has two constant terms: [tex]\(-9\)[/tex] and [tex]\(2\)[/tex].
- Combine these terms: [tex]\(-9 + 2 = -7\)[/tex].
After combining all the like terms, the expression simplifies to:
[tex]\[
5x^2 + 12x - 7
\][/tex]
Comparing this simplified expression with the multiple-choice options, we see that option B matches the simplified form exactly.
So, the equivalent expression is:
[tex]\[
\boxed{5x^2 + 12x - 7}
\][/tex]
