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