( a − 5 ) ( a + 5 ) + 3 a ( a − 7 ) (a

To simplify the expression \((a - 5)(a + 5) + 3a(a - 7)\), we will start by expanding each part.

1. Expand \((a - 5)(a + 5)\): This is the difference of squares: \[ (a - 5)(a + 5) = a^2 - 25 \]

2. Expand \(3a(a - 7)\): Distributing \(3a\) gives: \[ 3a(a - 7) = 3a^2 - 21a \]

3. Combine the results: Now we will add the two expanded expressions together: \[ a^2 - 25 + 3a^2 - 21a \] Combine like terms: \[ (a^2 + 3a^2) + (-21a) - 25 = 4a^2 - 21a - 25 \]

Thus, the simplified expression is: \[ \boxed{4a^2 - 21a - 25} \]