Answer
$$2(x-5)^2+2(x-5)+4=2x^2-18x+44$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x-5)^2+2(x-5)+4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x^2-10x+25)+2(x-5)+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^2-20x+50+2x-10+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^2-18x+40+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^2-18x+44\end{aligned} $$ | |
| ① | Find $ \left(x-5\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}{ 5 }$. $$ \begin{aligned}\left(x-5\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 5 + \color{red}{5^2} = x^2-10x+25\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x^2-10x+25\right) $ $$ \color{blue}{2} \cdot \left( x^2-10x+25\right) = 2x^2-20x+50 $$Multiply $ \color{blue}{2} $ by $ \left( x-5\right) $ $$ \color{blue}{2} \cdot \left( x-5\right) = 2x-10 $$ |
| ③ | Combine like terms: $$ 2x^2 \color{blue}{-20x} + \color{red}{50} + \color{blue}{2x} \color{red}{-10} = 2x^2 \color{blue}{-18x} + \color{red}{40} $$ |
| ④ | Combine like terms: $$ 2x^2-18x+ \color{blue}{40} + \color{blue}{4} = 2x^2-18x+ \color{blue}{44} $$ |
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