Let's analyze each of the expressions and equate them with the given options A, B, and C.
1. For the expression [tex]\((3x^2 - 7x + 14) + (5x^2 + 4x - 6)\)[/tex]:
First, we combine like terms:
[tex]\[
3x^2 + 5x^2 = 8x^2
\][/tex]
[tex]\[
-7x + 4x = -3x
\][/tex]
[tex]\[
14 - 6 = 8
\][/tex]
So, the expression simplifies to:
[tex]\[
8x^2 - 3x + 8
\][/tex]
Comparing this with the given expressions, we see that it matches expression [tex]\( B \)[/tex].
2. For the expression [tex]\((2x^2 - 5x - 3) + (-10x^2 + 2x + 7)\)[/tex]:
First, we combine like terms:
[tex]\[
2x^2 - 10x^2 = -8x^2
\][/tex]
[tex]\[
-5x + 2x = -3x
\][/tex]
[tex]\[
-3 + 7 = 4
\][/tex]
So, the expression simplifies to:
[tex]\[
-8x^2 - 3x + 4
\][/tex]
Comparing this with the given expressions, we see that it matches expression [tex]\( A \)[/tex].
3. For the expression [tex]\((12x^2 - 2x - 13) + (-4x^2 + 5x + 9)\)[/tex]:
First, we combine like terms:
[tex]\[
12x^2 - 4x^2 = 8x^2
\][/tex]
[tex]\[
-2x + 5x = 3x
\][/tex]
[tex]\[
-13 + 9 = -4
\][/tex]
So, the expression simplifies to:
[tex]\[
8x^2 + 3x - 4
\][/tex]
Comparing this with the given expressions, we see that it matches expression [tex]\( C \)[/tex].
Therefore, the correct answers are:
[tex]\[
(3x^2 - 7x + 14) + (5x^2 + 4x - 6) \text{ is equivalent to expression } \boxed{B}
\][/tex]
[tex]\[
(2x^2 - 5x - 3) + (-10x^2 + 2x + 7) \text{ is equivalent to expression } \boxed{A}
\][/tex]
[tex]\[
(12x^2 - 2x - 13) + (-4x^2 + 5x + 9) \text{ is equivalent to expression } \boxed{C}
\][/tex]
