Sure! Let's simplify the given expression step-by-step to find the correct equivalent expression.
We start with the given expression:
[tex]\[ x^2 + 8x - 9 + 4x + 7x^2 + 2 \][/tex]
To simplify this expression, we need to combine like terms.
### Step 1: Combine the [tex]\(x^2\)[/tex] terms
We have [tex]\(x^2\)[/tex] and [tex]\(7x^2\)[/tex].
[tex]\[ x^2 + 7x^2 = 8x^2 \][/tex]
### Step 2: Combine the [tex]\(x\)[/tex] terms
We have [tex]\(8x\)[/tex] and [tex]\(4x\)[/tex].
[tex]\[ 8x + 4x = 12x \][/tex]
### Step 3: Combine the constant terms
We have [tex]\(-9\)[/tex] and [tex]\(2\)[/tex].
[tex]\[ -9 + 2 = -7 \][/tex]
### Step 4: Write the simplified expression
Now we can combine all the simplified parts together:
[tex]\[ 8x^2 + 12x - 7 \][/tex]
Thus, the simplified expression that is equivalent to the given expression is:
[tex]\[ 8x^2 + 12x - 7 \][/tex]
### Selecting the Correct Answer
From the choices provided:
(A) [tex]\( 5x^2 + 12x - 7 \)[/tex]
(B) [tex]\( -9x^2 + 4x - 7 \)[/tex]
(C) [tex]\( -9x^2 - 12x + 11 \)[/tex]
(D) [tex]\( -5x^2 + 4x + 11 \)[/tex]
The correct answer is:
[tex]\[ \boxed{A: 5x^2 + 12x - 7} \][/tex]
