Question
Answer
$$(x-4)(x-6)(x-10)=x^3-20x^2+124x-240$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-4)(x-6)(x-10)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-6x-4x+24)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-10x+24)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-10x^2-10x^2+100x+24x-240 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-20x^2+124x-240\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-4}\right) $ by each term in $ \left( x-6\right) $. $$ \left( \color{blue}{x-4}\right) \cdot \left( x-6\right) = x^2-6x-4x+24 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-6x} \color{blue}{-4x} +24 = x^2 \color{blue}{-10x} +24 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-10x+24}\right) $ by each term in $ \left( x-10\right) $. $$ \left( \color{blue}{x^2-10x+24}\right) \cdot \left( x-10\right) = x^3-10x^2-10x^2+100x+24x-240 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-10x^2} \color{blue}{-10x^2} + \color{red}{100x} + \color{red}{24x} -240 = x^3 \color{blue}{-20x^2} + \color{red}{124x} -240 $$ |
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