Question
Answer
$$(x^2+10x+1)(x^2-3x+11)=x^4+7x^3-18x^2+107x+11$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+10x+1)(x^2-3x+11)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4+7x^3-18x^2+107x+11\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+10x+1}\right) $ by each term in $ \left( x^2-3x+11\right) $. $$ \left( \color{blue}{x^2+10x+1}\right) \cdot \left( x^2-3x+11\right) = x^4-3x^3+11x^2+10x^3-30x^2+110x+x^2-3x+11 $$ |
| ② | Combine like terms: $$ x^4 \color{blue}{-3x^3} + \color{red}{11x^2} + \color{blue}{10x^3} \color{green}{-30x^2} + \color{orange}{110x} + \color{green}{x^2} \color{orange}{-3x} +11 = \\ = x^4+ \color{blue}{7x^3} \color{green}{-18x^2} + \color{orange}{107x} +11 $$ |
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