Question
Answer
$$(x^2-10x+26)(x^3+6x^2+11x+30)=x^5-4x^4-23x^3+76x^2-14x+780$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-10x+26)(x^3+6x^2+11x+30)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^5-4x^4-23x^3+76x^2-14x+780\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-10x+26}\right) $ by each term in $ \left( x^3+6x^2+11x+30\right) $. $$ \left( \color{blue}{x^2-10x+26}\right) \cdot \left( x^3+6x^2+11x+30\right) = \\ = x^5+6x^4+11x^3+30x^2-10x^4-60x^3-110x^2-300x+26x^3+156x^2+286x+780 $$ |
| ② | Combine like terms: $$ x^5+ \color{blue}{6x^4} + \color{red}{11x^3} + \color{green}{30x^2} \color{blue}{-10x^4} \color{orange}{-60x^3} \color{blue}{-110x^2} \color{red}{-300x} + \color{orange}{26x^3} + \color{blue}{156x^2} + \color{red}{286x} +780 = \\ = x^5 \color{blue}{-4x^4} \color{orange}{-23x^3} + \color{blue}{76x^2} \color{red}{-14x} +780 $$ |
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