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