To simplify the expression \((a^2 - 11) + (3a^2 - 4a + 6)\), you can combine like terms.
First, distribute the addition across the terms:
\[ a^2 - 11 + 3a^2 - 4a + 6 \]
Now, group the like terms:
- Quadratic terms: \(a^2\) and \(3a^2\)
- Linear term: \(-4a\)
- Constant terms: \(-11\) and \(6\)
Now, combine these:
- For the \(a^2\) terms: \(a^2 + 3a^2 = 4a^2\)
- For the \(a\) term: \(-4a\) (remains as it is)
- For the constants: \(-11 + 6 = -5\)
Putting it all together, the simplified expression is:
\[ 4a^2 - 4a - 5 \]