(а+3) +(a-3)(а+3)+ба

To simplify the expression \((a + 3) + (a - 3)(a + 3) + ba\), we will first expand the second term \((a - 3)(a + 3)\) using the difference of squares formula:

\[ (a - 3)(a + 3) = a^2 - 9 \]

Now substituting back into the expression:

\[ (a + 3) + (a^2 - 9) + ba \]

Next, combine like terms:

1. The linear terms: \(a + 3 - 9 = a - 6\)
2. The quadratic term: \(a^2\)
3. The \(ba\) term stays as is.

So the expression simplifies to:

\[ a^2 + ba + (a - 6) \]

Thus, the final simplified expression is:

\[ a^2 + ba + a - 6 \]

Or simply:

\[ a^2 + (b + 1)a - 6 \]