Question
Answer
$$2(x+1)^2-2(x+1)-3=2x^2+2x-3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x+1)^2-2(x+1)-3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x^2+2x+1)-2(x+1)-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^2+4x+2-(2x+2)-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^2+4x+2-2x-2-3 \xlongequal{ } \\[1 em] & \xlongequal{ }2x^2+4x+ \cancel{2}-2x -\cancel{2}-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^2+2x-3\end{aligned} $$ | |
| ① | Find $ \left(x+1\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}{ 1 }$. $$ \begin{aligned}\left(x+1\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 1 + \color{red}{1^2} = x^2+2x+1\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x^2+2x+1\right) $ $$ \color{blue}{2} \cdot \left( x^2+2x+1\right) = 2x^2+4x+2 $$Multiply $ \color{blue}{2} $ by $ \left( x+1\right) $ $$ \color{blue}{2} \cdot \left( x+1\right) = 2x+2 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2x+2 \right) = -2x-2 $$ |
| ④ | Combine like terms: $$ 2x^2+ \color{blue}{4x} + \, \color{red}{ \cancel{2}} \, \color{blue}{-2x} \, \color{orange}{ -\cancel{2}} \, \color{orange}{-3} = 2x^2+ \color{blue}{2x} \color{orange}{-3} $$ |
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