(а+1) (а-1)(а2+1)-(9+а2) 2

To simplify the expression \((a+1)(a-1)(a^2+1) - (9+a^2)2\), we can start by expanding both parts of the expression. 1. **Expand \((a + 1)(a - 1)(a^2 + 1)\)**: - First, expand \((a + 1)(a - 1)\): \[ (a + 1)(a - 1) = a^2 - 1 \] - Now, substitute this result into \((a^2 - 1)(a^2 + 1)\): \[ (a^2 - 1)(a^2 + 1) = a^4 + a^2 - a^2 - 1 = a^4 - 1 \] 2. **Expand \((9 + a^2)2\)**: - Distribute the \(\2\): \[ (9 + a^2)2 = 2 \times 9 + 2 \times a^2 = 18 + 2a^2 \] 3. **Combine the two parts**: Now we substitute the expanded expressions back into the original equation: \[ (a^4 - 1) - (18 + 2a^2) \] Distributing the negative sign: \[ a^4 - 1 - 18 - 2a^2 = a^4 - 2a^2 - 19 \] So the simplified expression is: \[ \boxed{a^4 - 2a^2 - 19} \]