To perform polynomial addition, we need to combine like terms from both polynomials. Let's break down the expression step by step.
We have: \[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) \]
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Identify like terms:
- \(2x^2\) and \(3x^2\)
- \(6x\) and \(3x\)
- \(1\) and \(9\)
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Add the coefficients of like terms:
- For \(x^2\) terms: \(2 + 3 = 5\) so it becomes \(5x^2\)
- For \(x\) terms: \(6 + 3 = 9\) so it becomes \(9x\)
- For constant terms: \(1 + 9 = 10\) so it becomes \(10\)
Putting it all together, we get: \[ 5x^2 + 9x + 10 \]
So the correct statement representing polynomial addition is: \[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \]
Thus, the first response is the correct demonstration of polynomial addition.