Question
Answer
$$(x-2)^2+5(x-2)-1=x^2+x-7$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)^2+5(x-2)-1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2-4x+4+5(x-2)-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2-4x+4+5x-10-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^2+x-6-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^2+x-7\end{aligned} $$ | |
| 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}{5} $ by $ \left( x-2\right) $ $$ \color{blue}{5} \cdot \left( x-2\right) = 5x-10 $$ |
| ③ | Combine like terms: $$ x^2 \color{blue}{-4x} + \color{red}{4} + \color{blue}{5x} \color{red}{-10} = x^2+ \color{blue}{x} \color{red}{-6} $$ |
| ④ | Combine like terms: $$ x^2+x \color{blue}{-6} \color{blue}{-1} = x^2+x \color{blue}{-7} $$ |
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