First, let's simplify each given expression step by step and match the results to the expressions A, B, and C.
### Expression 1: [tex]\( (7x^2 - 5x + 3) + (2x^2 + 3x - 1) \)[/tex]
1. Combine the like terms for [tex]\(x^2\)[/tex]:
[tex]\[
7x^2 + 2x^2 = 9x^2
\][/tex]
2. Combine the like terms for [tex]\(x\)[/tex]:
[tex]\[
-5x + 3x = -2x
\][/tex]
3. Combine the constant terms:
[tex]\[
3 - 1 = 2
\][/tex]
So, the simplified expression is:
[tex]\[
9x^2 - 2x + 2
\][/tex]
This matches with expression [tex]\(B\)[/tex].
### Expression 2: [tex]\( (3x^2 - 4x - 4) + (-12x^2 + 2x + 11) \)[/tex]
1. Combine the like terms for [tex]\(x^2\)[/tex]:
[tex]\[
3x^2 - 12x^2 = -9x^2
\][/tex]
2. Combine the like terms for [tex]\(x\)[/tex]:
[tex]\[
-4x + 2x = -2x
\][/tex]
3. Combine the constant terms:
[tex]\[
-4 + 11 = 7
\][/tex]
So, the simplified expression is:
[tex]\[
-9x^2 - 2x + 7
\][/tex]
This matches with expression [tex]\(A\)[/tex].
### Expression 3: [tex]\( (4x^2 - 3x - 9) + (5x^2 + 5x + 2) \)[/tex]
1. Combine the like terms for [tex]\(x^2\)[/tex]:
[tex]\[
4x^2 + 5x^2 = 9x^2
\][/tex]
2. Combine the like terms for [tex]\(x\)[/tex]:
[tex]\[
-3x + 5x = 2x
\][/tex]
3. Combine the constant terms:
[tex]\[
-9 + 2 = -7
\][/tex]
So, the simplified expression is:
[tex]\[
9x^2 + 2x - 7
\][/tex]
This matches with expression [tex]\(C\)[/tex].
In summary:
- [tex]\( (7x^2 - 5x + 3) + (2x^2 + 3x - 1) \)[/tex] is equivalent to expression [tex]\( B \)[/tex].
- [tex]\( (3x^2 - 4x - 4) + (-12x^2 + 2x + 11) \)[/tex] is equivalent to expression [tex]\( A \)[/tex].
- [tex]\( (4x^2 - 3x - 9) + (5x^2 + 5x + 2) \)[/tex] is equivalent to expression [tex]\( C \)[/tex].
Thus, the completed statements are:
[tex]\[
\left(7 x^2-5 x+3\right)+\left(2 x^2+3 x-1\right) \text{ is equivalent to expression } \mathbf{B}
\][/tex]
[tex]\[
\left(3 x^2-4 x-4\right)+\left(-12 x^2+2 x+11\right) \text{ is equivalent to expression } \mathbf{A}
\][/tex]
[tex]\[
\left(4 x^2-3 x-9\right)+\left(5 x^2+5 x+2\right) \text{ is equivalent to expression } \mathbf{C}
\][/tex]
