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Consider the expressions shown below.

[tex]\[
\begin{array}{|c|c|c|}
\hline
A & B & C \\
\hline
-8x^2 - 3x + 4 & 8x^2 - 3x + 8 & 8x^2 + 3x - 4 \\
\hline
\end{array}
\][/tex]

Complete each of the following statements with the letter that represents the expression.

1. [tex]\((3x^2 - 7x + 14) + (5x^2 + 4x - 6)\)[/tex] is equivalent to expression [tex]\(\square\)[/tex].

2. [tex]\((2x^2 - 5x - 3) + (-10x^2 + 2x + 7)\)[/tex] is equivalent to expression [tex]\(\square\)[/tex].

3. [tex]\((12x^2 - 2x - 13) + (-4x^2 + 5x + 9)\)[/tex] is equivalent to expression [tex]\(\square\)[/tex].

Sagot :

GinnyAnsweridn
Let's examine each of the given expressions and match them with the provided expressions A, B, and C.

1. For the expression [tex]\( (3x^2 - 7x + 14) + (5x^2 + 4x - 6) \)[/tex]:
- Combine like terms:
[tex]\[ (3x^2 + 5x^2) + (-7x + 4x) + (14 - 6) = 8x^2 - 3x + 8 \][/tex]
- This matches expression [tex]\( B \)[/tex].

2. For the expression [tex]\( (2x^2 - 5x - 3) + (-10x^2 + 2x + 7) \)[/tex]:
- Combine like terms:
[tex]\[ (2x^2 - 10x^2) + (-5x + 2x) + (-3 + 7) = -8x^2 - 3x + 4 \][/tex]
- This matches expression [tex]\( A \)[/tex].

3. For the expression [tex]\( (12x^2 - 2x - 13) + (-4x^2 + 5x + 9) \)[/tex]:
- Combine like terms:
[tex]\[ (12x^2 - 4x^2) + (-2x + 5x) + (-13 + 9) = 8x^2 + 3x - 4 \][/tex]
- This matches expression [tex]\( C \)[/tex].

Therefore, the correct answers are:
[tex]\[ \boxed{B} \][/tex]
[tex]\[ \boxed{A} \][/tex]
[tex]\[ \boxed{C} \][/tex]
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