Answer
$$4(3x-2)(2x+3)^2=48x^3+112x^2+12x-72$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4(3x-2)(2x+3)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4(3x-2)(4x^2+12x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(12x-8)(4x^2+12x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}48x^3+144x^2+108x-32x^2-96x-72 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}48x^3+112x^2+12x-72\end{aligned} $$ | |
| ① | Find $ \left(2x+3\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2x } $ and $ B = \color{red}{ 3 }$. $$ \begin{aligned}\left(2x+3\right)^2 = \color{blue}{\left( 2x \right)^2} +2 \cdot 2x \cdot 3 + \color{red}{3^2} = 4x^2+12x+9\end{aligned} $$ |
| ② | Multiply $ \color{blue}{4} $ by $ \left( 3x-2\right) $ $$ \color{blue}{4} \cdot \left( 3x-2\right) = 12x-8 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{12x-8}\right) $ by each term in $ \left( 4x^2+12x+9\right) $. $$ \left( \color{blue}{12x-8}\right) \cdot \left( 4x^2+12x+9\right) = 48x^3+144x^2+108x-32x^2-96x-72 $$ |
| ④ | Combine like terms: $$ 48x^3+ \color{blue}{144x^2} + \color{red}{108x} \color{blue}{-32x^2} \color{red}{-96x} -72 = 48x^3+ \color{blue}{112x^2} + \color{red}{12x} -72 $$ |
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