Question
Answer
$$(x+6)(x-10)(x-18)=x^3-22x^2+12x+1080$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+6)(x-10)(x-18)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-10x+6x-60)(x-18) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-4x-60)(x-18) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-18x^2-4x^2+72x-60x+1080 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-22x^2+12x+1080\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+6}\right) $ by each term in $ \left( x-10\right) $. $$ \left( \color{blue}{x+6}\right) \cdot \left( x-10\right) = x^2-10x+6x-60 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-10x} + \color{blue}{6x} -60 = x^2 \color{blue}{-4x} -60 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-4x-60}\right) $ by each term in $ \left( x-18\right) $. $$ \left( \color{blue}{x^2-4x-60}\right) \cdot \left( x-18\right) = x^3-18x^2-4x^2+72x-60x+1080 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-18x^2} \color{blue}{-4x^2} + \color{red}{72x} \color{red}{-60x} +1080 = x^3 \color{blue}{-22x^2} + \color{red}{12x} +1080 $$ |
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