Answer
$$(x+2)^2-2(x-1)(x+3)=-x^2+10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2)^2-2(x-1)(x+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2+4x+4-2(x-1)(x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2+4x+4-(2x-2)(x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^2+4x+4-(2x^2+6x-2x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^2+4x+4-(2x^2+4x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}x^2+4x+4-2x^2-4x+6 \xlongequal{ } \\[1 em] & \xlongequal{ }x^2+ \cancel{4x}+4-2x^2 -\cancel{4x}+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-x^2+10\end{aligned} $$ | |
| 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-1\right) $ $$ \color{blue}{2} \cdot \left( x-1\right) = 2x-2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x-2}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{2x-2}\right) \cdot \left( x+3\right) = 2x^2+6x-2x-6 $$ |
| ④ | Combine like terms: $$ 2x^2+ \color{blue}{6x} \color{blue}{-2x} -6 = 2x^2+ \color{blue}{4x} -6 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2x^2+4x-6 \right) = -2x^2-4x+6 $$ |
| ⑥ | Combine like terms: $$ \color{blue}{x^2} + \, \color{red}{ \cancel{4x}} \,+ \color{orange}{4} \color{blue}{-2x^2} \, \color{red}{ -\cancel{4x}} \,+ \color{orange}{6} = \color{blue}{-x^2} + \color{orange}{10} $$ |
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