Question
Answer
$$(1+2x+3x^2)\cdot4\cdot(2+2x)\cdot2=48x^3+80x^2+48x+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+2x+3x^2)\cdot4\cdot(2+2x)\cdot2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4+8x+12x^2)\cdot(2+2x)\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(8+8x+16x+16x^2+24x^2+24x^3)\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(24x^3+40x^2+24x+8)\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}48x^3+80x^2+48x+16\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{1+2x+3x^2}\right) \cdot 4 = 4+8x+12x^2 $$ |
| ② | Multiply each term of $ \left( \color{blue}{4+8x+12x^2}\right) $ by each term in $ \left( 2+2x\right) $. $$ \left( \color{blue}{4+8x+12x^2}\right) \cdot \left( 2+2x\right) = 8+8x+16x+16x^2+24x^2+24x^3 $$ |
| ③ | Combine like terms: $$ 8+ \color{blue}{8x} + \color{blue}{16x} + \color{red}{16x^2} + \color{red}{24x^2} +24x^3 = 24x^3+ \color{red}{40x^2} + \color{blue}{24x} +8 $$ |
| ④ | $$ \left( \color{blue}{24x^3+40x^2+24x+8}\right) \cdot 2 = 48x^3+80x^2+48x+16 $$ |
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