Question
Answer
$$2(x-2)^2+4(x-2)-6=2x^2-4x-6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x-2)^2+4(x-2)-6& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x^2-4x+4)+4(x-2)-6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^2-8x+8+4x-8-6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^2-4x-6\end{aligned} $$ | |
| ① | Find $ \left(x-2\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}{ 2 }$. $$ \begin{aligned}\left(x-2\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 2 + \color{red}{2^2} = x^2-4x+4\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x^2-4x+4\right) $ $$ \color{blue}{2} \cdot \left( x^2-4x+4\right) = 2x^2-8x+8 $$Multiply $ \color{blue}{4} $ by $ \left( x-2\right) $ $$ \color{blue}{4} \cdot \left( x-2\right) = 4x-8 $$ |
| ③ | Combine like terms: $$ 2x^2 \color{blue}{-8x} + \, \color{red}{ \cancel{8}} \,+ \color{blue}{4x} \, \color{red}{ -\cancel{8}} \, = 2x^2 \color{blue}{-4x} $$ |
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