Let's simplify the left-hand side of the equation step by step:
- Combine the terms from the first expression \( (2x^2 + 6x + 1) \) and the second expression \( (3x^2 + 3x + 9) \):
\[ 2x^2 + 6x + 1 + 3x^2 + 3x + 9 \]
- Combine like terms:
- For the \( x^2 \) terms: \( 2x^2 + 3x^2 = 5x^2 \)
- For the \( x \) terms: \( 6x + 3x = 9x \)
- For the constant terms: \( 1 + 9 = 10 \)
Putting it all together, we have:
\[ 5x^2 + 9x + 10 \]
Now, we compare this result with the right-hand side of the equation \( 5x^2 + 9x + 10 \).
Both sides are indeed equal:
\[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \]
Therefore, the statement is True.