Answer
The simplified form is $9{{x}^{2}}-30x+30$.
Work Step by Step
The given expression can be simplified using the property of squares:
${{\left( a-b \right)}^{2}}={{a}^{2}}+{{b}^{2}}-2ab$
Simply as below:
$\begin{align}
& {{\left( f\left( x \right) \right)}^{2}}-2f\left( x \right)+6={{\left( 3x-4 \right)}^{2}}-2\left( 3x-4 \right)+6 \\
& ={{\left( 3x \right)}^{2}}+{{4}^{2}}-2\cdot 3x\cdot 4-2\cdot 3x-2\cdot \left( -4 \right)+6 \\
& =9{{x}^{2}}+16-24x-6x+8+6 \\
& =9{{x}^{2}}-30x+30
\end{align}$
Thus, the simplified form is $9{{x}^{2}}-30x+30$.
