Answer
$$(x+2)^2+4(x+2)+6=x^2+8x+18$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2)^2+4(x+2)+6& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2+4x+4+4(x+2)+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2+4x+4+4x+8+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^2+8x+12+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^2+8x+18\end{aligned} $$ | |
| 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}{4} $ by $ \left( x+2\right) $ $$ \color{blue}{4} \cdot \left( x+2\right) = 4x+8 $$ |
| ③ | Combine like terms: $$ x^2+ \color{blue}{4x} + \color{red}{4} + \color{blue}{4x} + \color{red}{8} = x^2+ \color{blue}{8x} + \color{red}{12} $$ |
| ④ | Combine like terms: $$ x^2+8x+ \color{blue}{12} + \color{blue}{6} = x^2+8x+ \color{blue}{18} $$ |
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