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