To correctly demonstrate polynomial subtraction for the expression \( (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \), we need to distribute the negative sign to each term in the second polynomial and then combine like terms.
Let's perform the subtraction step by step:
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Write the expression: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \]
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Distribute the negative sign: \[ = 2x^2 + 6x + 1 - 3x^2 - 3x - 9 \]
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Now, combine like terms:
- For the \(x^2\) terms: \( 2x^2 - 3x^2 = -x^2 \)
- For the \(x\) terms: \( 6x - 3x = 3x \)
- For the constant terms: \( 1 - 9 = -8 \)
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Putting it all together: \[ -x^2 + 3x - 8 \]
Therefore, the correct answer is: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8 \]
So, the second option is correct: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8 \]
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