Question
Answer
$$(x-2)(x+3)(x^2-5x+1)=x^4-4x^3-10x^2+31x-6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)(x+3)(x^2-5x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+3x-2x-6)(x^2-5x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+x-6)(x^2-5x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4-4x^3-10x^2+31x-6\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-2}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x-2}\right) \cdot \left( x+3\right) = x^2+3x-2x-6 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{3x} \color{blue}{-2x} -6 = x^2+ \color{blue}{x} -6 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+x-6}\right) $ by each term in $ \left( x^2-5x+1\right) $. $$ \left( \color{blue}{x^2+x-6}\right) \cdot \left( x^2-5x+1\right) = x^4-5x^3+x^2+x^3-5x^2+x-6x^2+30x-6 $$ |
| ④ | Combine like terms: $$ x^4 \color{blue}{-5x^3} + \color{red}{x^2} + \color{blue}{x^3} \color{green}{-5x^2} + \color{orange}{x} \color{green}{-6x^2} + \color{orange}{30x} -6 = \\ = x^4 \color{blue}{-4x^3} \color{green}{-10x^2} + \color{orange}{31x} -6 $$ |
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