To correctly demonstrate polynomial addition, we need to add the like terms from the two polynomials.
Let's simplify the expression \((2x^2 + 6x + 1) + (3x^2 + 3x + 9)\):
1. Combine the \(x^2\) terms:
\[
2x^2 + 3x^2 = 5x^2
\]
2. Combine the \(x\) terms:
\[
6x + 3x = 9x
\]
3. Combine the constant terms:
\[
1 + 9 = 10
\]
Putting it all together, we get:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]
So the correct answer is:
\((2x^2+6x+1)+(3x^2+3x+9)=5x^2+9x+10\)