Question
Answer
$$(x-8)(x-6)(x-4)(x+2)=x^4-16x^3+68x^2+16x-384$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-8)(x-6)(x-4)(x+2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-6x-8x+48)(x-4)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-14x+48)(x-4)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3-4x^2-14x^2+56x+48x-192)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3-18x^2+104x-192)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^4-16x^3+68x^2+16x-384\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-8}\right) $ by each term in $ \left( x-6\right) $. $$ \left( \color{blue}{x-8}\right) \cdot \left( x-6\right) = x^2-6x-8x+48 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-6x} \color{blue}{-8x} +48 = x^2 \color{blue}{-14x} +48 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-14x+48}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x^2-14x+48}\right) \cdot \left( x-4\right) = x^3-4x^2-14x^2+56x+48x-192 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-4x^2} \color{blue}{-14x^2} + \color{red}{56x} + \color{red}{48x} -192 = x^3 \color{blue}{-18x^2} + \color{red}{104x} -192 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3-18x^2+104x-192}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x^3-18x^2+104x-192}\right) \cdot \left( x+2\right) = x^4+2x^3-18x^3-36x^2+104x^2+208x-192x-384 $$ |
| ⑥ | Combine like terms: $$ x^4+ \color{blue}{2x^3} \color{blue}{-18x^3} \color{red}{-36x^2} + \color{red}{104x^2} + \color{green}{208x} \color{green}{-192x} -384 = \\ = x^4 \color{blue}{-16x^3} + \color{red}{68x^2} + \color{green}{16x} -384 $$ |
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