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Fill in the blanks to complete the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference. (2 points) 9x2 + x + 13 – 2x2 + 12x + x2 + 5x + 2

7 answers

To complete the polynomial equation showing the subtraction of the second expression from the first, we start with the given expression:

The first expression is: \[ 9x^2 + x + 13 \]

The second expression is: \[ 2x^2 + 12x + x^2 + 5x + 2 \]

First, we combine like terms in the second expression: \[ 2x^2 + x^2 = 3x^2 \] \[ 12x + 5x = 17x \]

So, the second expression simplifies to: \[ 3x^2 + 17x + 2 \]

Now we write the subtraction: \[ (9x^2 + x + 13) - (3x^2 + 17x + 2) \]

This results in:

  1. Subtract the \(x^2\) terms: \[ 9x^2 - 3x^2 = 6x^2 \]

  2. Subtract the \(x\) terms: \[ x - 17x = -16x \]

  3. Subtract the constant terms: \[ 13 - 2 = 11 \]

Putting it all together, the final expression after the subtraction is: \[ 6x^2 - 16x + 11 \]

Thus, the completed polynomial equation is: \[ 9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11 \]

That is incorrect

Let's carefully go through the subtraction step by step again.

We start with the expressions provided:

  1. First expression: \[ 9x^2 + x + 13 \]

  2. Second expression: \[ 2x^2 + 12x + x^2 + 5x + 2 \]

First, let's combine like terms in the second expression:

  • Combine \(2x^2\) and \(x^2\): \[ 2x^2 + x^2 = 3x^2 \]

  • Combine \(12x\) and \(5x\): \[ 12x + 5x = 17x \]

So the second expression simplifies to: \[ 3x^2 + 17x + 2 \]

Now we perform the subtraction:

\[ (9x^2 + x + 13) - (3x^2 + 17x + 2) \]

Now we subtract each corresponding term:

  1. For \(x^2\) terms: \[ 9x^2 - 3x^2 = 6x^2 \]

  2. For \(x\) terms: \[ x - 17x = -16x \]

  3. For constant terms: \[ 13 - 2 = 11 \]

Putting it all together, we have: \[ 6x^2 - 16x + 11 \]

So the correctly completed polynomial equation showing the subtraction of the second expression from the first is:

\[ 9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11 \]

Please let me know if this explanation clarifies the process or if you have further questions.

That is the same answer, it is incorrect.

I apologize for the confusion earlier. Let's reevaluate the problem step by step to ensure we arrive at the correct answer.

We have the following expressions:

  1. First expression:
    \[ 9x^2 + x + 13 \]

  2. Second expression:
    \[ 2x^2 + 12x + x^2 + 5x + 2 \]

Step 1: Combine like terms in the second expression.

  • For the \(x^2\) terms:
    \[ 2x^2 + x^2 = 3x^2 \]

  • For the \(x\) terms:
    \[ 12x + 5x = 17x \]

  • The constant term is:
    \[ 2 \]

Thus, the second expression simplifies to:
\[ 3x^2 + 17x + 2 \]

Step 2: Perform the subtraction.
Now we will subtract the second expression from the first:

\[ (9x^2 + x + 13) - (3x^2 + 17x + 2) \]

Distributing the negative sign across the second expression:

\[ = 9x^2 + x + 13 - 3x^2 - 17x - 2 \]

Step 3: Combine like terms.

  • For the \(x^2\) terms:
    \[ 9x^2 - 3x^2 = 6x^2 \]

  • For the \(x\) terms:
    \[ x - 17x = -16x \]

  • For the constant terms:
    \[ 13 - 2 = 11 \]

Putting it all together, we get:

\[ 6x^2 - 16x + 11 \]

Final Result:

The correct subtraction statement is:

\[ 9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11 \]

If you have an alternative expression or requirement that I'm missing, please clarify, and I'll be glad to assist!

It's still incorrect!!

Apologies for the misunderstanding. Let's work through the problem from the beginning again with careful attention to all details.

Given expressions:

  1. First expression:
    \[ 9x^2 + x + 13 \]

  2. Second expression:
    \[ 2x^2 + 12x + x^2 + 5x + 2 \]

Step 1: Combine like terms in the second expression.

Let’s simplify the second expression:

  • Combine \(2x^2\) and \(x^2\): \[ 2x^2 + 1x^2 = 3x^2 \]

  • Combine \(12x\) and \(5x\): \[ 12x + 5x = 17x \]

So the second expression simplifies to: \[ 3x^2 + 17x + 2 \]

Step 2: Subtract the second expression from the first.

Now we need to subtract the second expression from the first: \[ (9x^2 + x + 13) - (3x^2 + 17x + 2) \]

Step 3: Distribute the negative sign.

This gives us: \[ 9x^2 + x + 13 - 3x^2 - 17x - 2 \]

Step 4: Combine like terms.

Now, let's combine the terms together:

  1. For \(x^2\): \[ 9x^2 - 3x^2 = 6x^2 \]

  2. For \(x\): \[ x - 17x = -16x \]

  3. For constants: \[ 13 - 2 = 11 \]

Putting all these together, we have: \[ 6x^2 - 16x + 11 \]

Summary of the polynomial equation:

Thus, the complete polynomial equation that shows the subtraction of the second expression from the first is: \[ 9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11 \]

If there's an error in understanding the expressions or any specific details, please clarify. Thank you for your patience!