Question
Answer
$$(1+2x+3x^2)(4+5x+6x^2)=18x^4+27x^3+28x^2+13x+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+2x+3x^2)(4+5x+6x^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}18x^4+27x^3+28x^2+13x+4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{1+2x+3x^2}\right) $ by each term in $ \left( 4+5x+6x^2\right) $. $$ \left( \color{blue}{1+2x+3x^2}\right) \cdot \left( 4+5x+6x^2\right) = 4+5x+6x^2+8x+10x^2+12x^3+12x^2+15x^3+18x^4 $$ |
| ② | Combine like terms: $$ 4+ \color{blue}{5x} + \color{red}{6x^2} + \color{blue}{8x} + \color{green}{10x^2} + \color{orange}{12x^3} + \color{green}{12x^2} + \color{orange}{15x^3} +18x^4 = \\ = 18x^4+ \color{orange}{27x^3} + \color{green}{28x^2} + \color{blue}{13x} +4 $$ |
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