Question
Answer
$$(x-4)(x-8)(x-10)=x^3-22x^2+152x-320$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-4)(x-8)(x-10)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-8x-4x+32)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-12x+32)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-10x^2-12x^2+120x+32x-320 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-22x^2+152x-320\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-4}\right) $ by each term in $ \left( x-8\right) $. $$ \left( \color{blue}{x-4}\right) \cdot \left( x-8\right) = x^2-8x-4x+32 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-8x} \color{blue}{-4x} +32 = x^2 \color{blue}{-12x} +32 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-12x+32}\right) $ by each term in $ \left( x-10\right) $. $$ \left( \color{blue}{x^2-12x+32}\right) \cdot \left( x-10\right) = x^3-10x^2-12x^2+120x+32x-320 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-10x^2} \color{blue}{-12x^2} + \color{red}{120x} + \color{red}{32x} -320 = x^3 \color{blue}{-22x^2} + \color{red}{152x} -320 $$ |
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