Question
Answer
$$(x-4)(x+2)(3x+1)=3x^3-5x^2-26x-8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-4)(x+2)(3x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x-4x-8)(3x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-2x-8)(3x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3x^3+x^2-6x^2-2x-24x-8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3x^3-5x^2-26x-8\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-4}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x-4}\right) \cdot \left( x+2\right) = x^2+2x-4x-8 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{2x} \color{blue}{-4x} -8 = x^2 \color{blue}{-2x} -8 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-2x-8}\right) $ by each term in $ \left( 3x+1\right) $. $$ \left( \color{blue}{x^2-2x-8}\right) \cdot \left( 3x+1\right) = 3x^3+x^2-6x^2-2x-24x-8 $$ |
| ④ | Combine like terms: $$ 3x^3+ \color{blue}{x^2} \color{blue}{-6x^2} \color{red}{-2x} \color{red}{-24x} -8 = 3x^3 \color{blue}{-5x^2} \color{red}{-26x} -8 $$ |
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