Question
Answer
$$2(x+4)^2+4(x+4)+4=2x^2+20x+52$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x+4)^2+4(x+4)+4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x^2+8x+16)+4(x+4)+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^2+16x+32+4x+16+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^2+20x+48+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^2+20x+52\end{aligned} $$ | |
| ① | Find $ \left(x+4\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}{ 4 }$. $$ \begin{aligned}\left(x+4\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 4 + \color{red}{4^2} = x^2+8x+16\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x^2+8x+16\right) $ $$ \color{blue}{2} \cdot \left( x^2+8x+16\right) = 2x^2+16x+32 $$Multiply $ \color{blue}{4} $ by $ \left( x+4\right) $ $$ \color{blue}{4} \cdot \left( x+4\right) = 4x+16 $$ |
| ③ | Combine like terms: $$ 2x^2+ \color{blue}{16x} + \color{red}{32} + \color{blue}{4x} + \color{red}{16} = 2x^2+ \color{blue}{20x} + \color{red}{48} $$ |
| ④ | Combine like terms: $$ 2x^2+20x+ \color{blue}{48} + \color{blue}{4} = 2x^2+20x+ \color{blue}{52} $$ |
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