Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.6 - Transformations of Functions - Exercise Set - Page 245: 157


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 $9{{x}^{2}}-30x+30$.
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