Answer
$-7{{a}^{2}}+3a-8$
Work Step by Step
$\left( 2{{a}^{2}}-3a-7 \right)-\left( 9{{a}^{2}}-6a+1 \right)$,
Apply the rule of subtraction of polynomials,
$\left( 2{{a}^{2}}-3a-7 \right)-\left( 9{{a}^{2}}-6a+1 \right)=2{{a}^{2}}-3a-7-9{{a}^{2}}+6a-1$
Combining the like terms,
$\begin{align}
& \left( 2{{a}^{2}}-3a-7 \right)-\left( 9{{a}^{2}}-6a+1 \right)=\left( 2{{a}^{2}}-9{{a}^{2}} \right)+\left( -3a+6a \right)+\left( -7-1 \right) \\
& =-7{{a}^{2}}+3a-8
\end{align}$
Therefore, the simplified form of the expression is $-7{{a}^{2}}+3a-8$.
