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