Answer
$$2(x+2)^2-5(x+2)+3=2x^2+3x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x+2)^2-5(x+2)+3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x^2+4x+4)-5(x+2)+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^2+8x+8-(5x+10)+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^2+8x+8-5x-10+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^2+3x+1\end{aligned} $$ | |
| 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}{5} $ by $ \left( x+2\right) $ $$ \color{blue}{5} \cdot \left( x+2\right) = 5x+10 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 5x+10 \right) = -5x-10 $$ |
| ④ | Combine like terms: $$ 2x^2+ \color{blue}{8x} + \color{red}{8} \color{blue}{-5x} \color{green}{-10} + \color{green}{3} = 2x^2+ \color{blue}{3x} + \color{green}{1} $$ |
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