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Type the correct answer in each box.

Consider the expressions shown below.
\begin{tabular}{|c|c|c|}
\hline A & B & C \\
\hline[tex]$-7 x^2-2 x+5$[/tex] & [tex]$7 x^2-2 x+7$[/tex] & [tex]$7 x^2+2 x-5$[/tex] \\
\hline
\end{tabular}

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

[tex]\(\left(3 x^2-6 x+11\right)-\left(10 x^2-4 x+6\right)\)[/tex] is equivalent to expression [tex]\(\square\)[/tex]

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

[tex]\(\left(12 x^2+6 x-5\right)-\left(5 x^2+8 x-12\right)\)[/tex] is equivalent to expression [tex]\(\square\)[/tex]



Answer :

GinnyAnswer
Let's match the given expressions with A, B, and C step-by-step.

1. We need to determine which given expression:
[tex]\[ A = -7 x^2 - 2 x + 5 \][/tex]
[tex]\[ B = 7 x^2 - 2 x + 7 \][/tex]
[tex]\[ C = 7 x^2 + 2 x - 5 \][/tex]

2. First expression:
[tex]\[ (3 x^2 - 6 x + 11) - (10 x^2 - 4 x + 6) \][/tex]

Simplify this expression:
[tex]\[ 3 x^2 - 6 x + 11 - 10 x^2 + 4 x - 6 = (3 x^2 - 10 x^2) + (-6 x + 4 x) + (11 - 6) = -7 x^2 - 2 x + 5 \][/tex]

The simplified expression matches with [tex]\( A \)[/tex].

3. Second expression:
[tex]\[ (-3 x^2 - 5 x - 3) - (-10 x^2 - 7 x + 2) \][/tex]

Simplify this expression:
[tex]\[ -3 x^2 - 5 x - 3 + 10 x^2 + 7 x - 2 = (-3 x^2 + 10 x^2) + (-5 x + 7 x) + (-3 - 2) = 7 x^2 + 2 x - 5 \][/tex]

The simplified expression matches with [tex]\( C \)[/tex].

4. Third expression:
[tex]\[ (12 x^2 + 6 x - 5) - (5 x^2 + 8 x - 12) \][/tex]

Simplify this expression:
[tex]\[ 12 x^2 + 6 x - 5 - 5 x^2 - 8 x + 12 = (12 x^2 - 5 x^2) + (6 x - 8 x) + (-5 + 12) = 7 x^2 - 2 x + 7 \][/tex]

The simplified expression matches with [tex]\( B \)[/tex].

So, the complete statements are as follows:

[tex]\((3 x^2 - 6 x + 11) - (10 x^2 - 4 x + 6)\)[/tex] is equivalent to expression [tex]\( \mathbf{A} \)[/tex]
[tex]\(( -3 x^2 - 5 x - 3) - ( -10 x^2 - 7 x + 2)\)[/tex] is equivalent to expression [tex]\( \mathbf{C} \)[/tex]
[tex]\((12 x^2 + 6 x - 5) - (5 x^2 + 8 x - 12)\)[/tex] is equivalent to expression [tex]\( \mathbf{B} \)[/tex]

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