Question
Answer
$$(x-8)(x-15)(x-21)=x^3-44x^2+603x-2520$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-8)(x-15)(x-21)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-15x-8x+120)(x-21) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-23x+120)(x-21) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-21x^2-23x^2+483x+120x-2520 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-44x^2+603x-2520\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-8}\right) $ by each term in $ \left( x-15\right) $. $$ \left( \color{blue}{x-8}\right) \cdot \left( x-15\right) = x^2-15x-8x+120 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-15x} \color{blue}{-8x} +120 = x^2 \color{blue}{-23x} +120 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-23x+120}\right) $ by each term in $ \left( x-21\right) $. $$ \left( \color{blue}{x^2-23x+120}\right) \cdot \left( x-21\right) = x^3-21x^2-23x^2+483x+120x-2520 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-21x^2} \color{blue}{-23x^2} + \color{red}{483x} + \color{red}{120x} -2520 = x^3 \color{blue}{-44x^2} + \color{red}{603x} -2520 $$ |
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