Answer
$$(2x+2)(2x+3)^3=16x^4+88x^3+180x^2+162x+54$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x+2)(2x+3)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x+2)(8x^3+36x^2+54x+27) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}16x^4+88x^3+180x^2+162x+54\end{aligned} $$ | |
| ① | Find $ \left(2x+3\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 2x $ and $ B = 3 $. $$ \left(2x+3\right)^3 = \left( 2x \right)^3+3 \cdot \left( 2x \right)^2 \cdot 3 + 3 \cdot 2x \cdot 3^2+3^3 = 8x^3+36x^2+54x+27 $$ |
| ② | Multiply each term of $ \left( \color{blue}{2x+2}\right) $ by each term in $ \left( 8x^3+36x^2+54x+27\right) $. $$ \left( \color{blue}{2x+2}\right) \cdot \left( 8x^3+36x^2+54x+27\right) = 16x^4+72x^3+108x^2+54x+16x^3+72x^2+108x+54 $$ |
| ③ | Combine like terms: $$ 16x^4+ \color{blue}{72x^3} + \color{red}{108x^2} + \color{green}{54x} + \color{blue}{16x^3} + \color{red}{72x^2} + \color{green}{108x} +54 = \\ = 16x^4+ \color{blue}{88x^3} + \color{red}{180x^2} + \color{green}{162x} +54 $$ |
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