Answer
$$2(x-3)^2+2(x-3)-1=2x^2-10x+11$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x-3)^2+2(x-3)-1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x^2-6x+9)+2(x-3)-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^2-12x+18+2x-6-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^2-10x+12-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^2-10x+11\end{aligned} $$ | |
| ① | Find $ \left(x-3\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}{ 3 }$. $$ \begin{aligned}\left(x-3\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 3 + \color{red}{3^2} = x^2-6x+9\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x^2-6x+9\right) $ $$ \color{blue}{2} \cdot \left( x^2-6x+9\right) = 2x^2-12x+18 $$Multiply $ \color{blue}{2} $ by $ \left( x-3\right) $ $$ \color{blue}{2} \cdot \left( x-3\right) = 2x-6 $$ |
| ③ | Combine like terms: $$ 2x^2 \color{blue}{-12x} + \color{red}{18} + \color{blue}{2x} \color{red}{-6} = 2x^2 \color{blue}{-10x} + \color{red}{12} $$ |
| ④ | Combine like terms: $$ 2x^2-10x+ \color{blue}{12} \color{blue}{-1} = 2x^2-10x+ \color{blue}{11} $$ |
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