Question
Answer
$$(5x-3)(x+2)(x-8)=5x^3-33x^2-62x+48$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x-3)(x+2)(x-8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(5x^2+10x-3x-6)(x-8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(5x^2+7x-6)(x-8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5x^3-40x^2+7x^2-56x-6x+48 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}5x^3-33x^2-62x+48\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5x-3}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{5x-3}\right) \cdot \left( x+2\right) = 5x^2+10x-3x-6 $$ |
| ② | Combine like terms: $$ 5x^2+ \color{blue}{10x} \color{blue}{-3x} -6 = 5x^2+ \color{blue}{7x} -6 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{5x^2+7x-6}\right) $ by each term in $ \left( x-8\right) $. $$ \left( \color{blue}{5x^2+7x-6}\right) \cdot \left( x-8\right) = 5x^3-40x^2+7x^2-56x-6x+48 $$ |
| ④ | Combine like terms: $$ 5x^3 \color{blue}{-40x^2} + \color{blue}{7x^2} \color{red}{-56x} \color{red}{-6x} +48 = 5x^3 \color{blue}{-33x^2} \color{red}{-62x} +48 $$ |
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