Question
Answer
$$(x^2-5x+5)(x^2-3x+1)=x^4-8x^3+21x^2-20x+5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-5x+5)(x^2-3x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4-8x^3+21x^2-20x+5\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-5x+5}\right) $ by each term in $ \left( x^2-3x+1\right) $. $$ \left( \color{blue}{x^2-5x+5}\right) \cdot \left( x^2-3x+1\right) = x^4-3x^3+x^2-5x^3+15x^2-5x+5x^2-15x+5 $$ |
| ② | Combine like terms: $$ x^4 \color{blue}{-3x^3} + \color{red}{x^2} \color{blue}{-5x^3} + \color{green}{15x^2} \color{orange}{-5x} + \color{green}{5x^2} \color{orange}{-15x} +5 = \\ = x^4 \color{blue}{-8x^3} + \color{green}{21x^2} \color{orange}{-20x} +5 $$ |
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