Answer
$$6(x-1)^2-(x-1)=6x^2-13x+7$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6(x-1)^2-(x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6(x^2-2x+1)-(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6x^2-12x+6-(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6x^2-12x+6-x+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6x^2-13x+7\end{aligned} $$ | |
| ① | Find $ \left(x-1\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(x-1\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 1 + \color{red}{1^2} = x^2-2x+1\end{aligned} $$ |
| ② | Multiply $ \color{blue}{6} $ by $ \left( x^2-2x+1\right) $ $$ \color{blue}{6} \cdot \left( x^2-2x+1\right) = 6x^2-12x+6 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( x-1 \right) = -x+1 $$ |
| ④ | Combine like terms: $$ 6x^2 \color{blue}{-12x} + \color{red}{6} \color{blue}{-x} + \color{red}{1} = 6x^2 \color{blue}{-13x} + \color{red}{7} $$ |
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