Question
Answer
$$(x+2x+3x^2)\cdot4\cdot(2+2x)\cdot2=48x^3+96x^2+48x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2x+3x^2)\cdot4\cdot(2+2x)\cdot2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3x^2+3x)\cdot4\cdot(2+2x)\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(12x^2+12x)\cdot(2+2x)\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(24x^2+24x^3+24x+24x^2)\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(24x^3+48x^2+24x)\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}48x^3+96x^2+48x\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{x} + \color{blue}{2x} +3x^2 = 3x^2+ \color{blue}{3x} $$ |
| ② | $$ \left( \color{blue}{3x^2+3x}\right) \cdot 4 = 12x^2+12x $$ |
| ③ | Multiply each term of $ \left( \color{blue}{12x^2+12x}\right) $ by each term in $ \left( 2+2x\right) $. $$ \left( \color{blue}{12x^2+12x}\right) \cdot \left( 2+2x\right) = 24x^2+24x^3+24x+24x^2 $$ |
| ④ | Combine like terms: $$ \color{blue}{24x^2} +24x^3+24x+ \color{blue}{24x^2} = 24x^3+ \color{blue}{48x^2} +24x $$ |
| ⑤ | $$ \left( \color{blue}{24x^3+48x^2+24x}\right) \cdot 2 = 48x^3+96x^2+48x $$ |
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