Multiply. \( \left(a^{2}+a-1\right)\left(a^{2}+6 a-8\right) \) \( \left(a^{2}+a-1\right)\left(a^{2}+6 a-8\right)= \) (Simplify your answer.)

To multiply \( \left(a^{2}+a-1\right)\left(a^{2}+6 a-8\right) \), we will use the distributive property (also known as the FOIL method for binomials). 1. Start by distributing each term in the first polynomial to each term in the second polynomial: \[ \begin{align*} & a^{2} \cdot a^{2} + a^{2} \cdot 6a + a^{2} \cdot (-8) \\ & + a \cdot a^{2} + a \cdot 6a + a \cdot (-8) \\ & + (-1) \cdot a^{2} + (-1) \cdot 6a + (-1) \cdot (-8). \end{align*} \] 2. Now calculate each of these products: \[ \begin{align*} & a^{4} + 6a^{3} - 8a^{2} \\ & + a^{3} + 6a^{2} - 8a \\ & - a^{2} - 6a + 8. \end{align*} \] 3. Combine like terms: - The \( a^{4} \) term stands alone: \( a^{4} \). - The \( a^{3} \) terms combine as \( 6a^{3} + a^{3} = 7a^{3} \). - The \( a^{2} \) terms combine as \( -8a^{2} + 6a^{2} - a^{2} = -3a^{2} \). - The \( a \) terms combine as \( -8a - 6a = -14a \). - The constant is \( +8 \). Putting it all together, we get: \[ \left(a^{2}+a-1\right)\left(a^{2}+6 a-8\right) = a^{4} + 7a^{3} - 3a^{2} - 14a + 8. \] So, the final simplified answer is: \[ a^{4} + 7a^{3} - 3a^{2} - 14a + 8. \]