Question
Answer
$$(3t^3+a)^2(12t^3+a)=108t^9+81at^6+18a^2t^3+a^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3t^3+a)^2(12t^3+a)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(9t^6+6at^3+a^2)(12t^3+a) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}108t^9+9at^6+72at^6+6a^2t^3+12a^2t^3+a^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}108t^9+81at^6+18a^2t^3+a^3\end{aligned} $$ | |
| ① | Find $ \left(3t^3+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}{ 3t^3 } $ and $ B = \color{red}{ a }$. $$ \begin{aligned}\left(3t^3+a\right)^2 = \color{blue}{\left( 3t^3 \right)^2} +2 \cdot 3t^3 \cdot a + \color{red}{a^2} = 9t^6+6at^3+a^2\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{9t^6+6at^3+a^2}\right) $ by each term in $ \left( 12t^3+a\right) $. $$ \left( \color{blue}{9t^6+6at^3+a^2}\right) \cdot \left( 12t^3+a\right) = 108t^9+9at^6+72at^6+6a^2t^3+12a^2t^3+a^3 $$ |
| ③ | Combine like terms: $$ 108t^9+ \color{blue}{9at^6} + \color{blue}{72at^6} + \color{red}{6a^2t^3} + \color{red}{12a^2t^3} +a^3 = 108t^9+ \color{blue}{81at^6} + \color{red}{18a^2t^3} +a^3 $$ |
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