Answer
$$(5x-8)(3x+2)(x-6)=15x^3-104x^2+68x+96$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x-8)(3x+2)(x-6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(15x^2+10x-24x-16)(x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(15x^2-14x-16)(x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}15x^3-90x^2-14x^2+84x-16x+96 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}15x^3-104x^2+68x+96\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5x-8}\right) $ by each term in $ \left( 3x+2\right) $. $$ \left( \color{blue}{5x-8}\right) \cdot \left( 3x+2\right) = 15x^2+10x-24x-16 $$ |
| ② | Combine like terms: $$ 15x^2+ \color{blue}{10x} \color{blue}{-24x} -16 = 15x^2 \color{blue}{-14x} -16 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{15x^2-14x-16}\right) $ by each term in $ \left( x-6\right) $. $$ \left( \color{blue}{15x^2-14x-16}\right) \cdot \left( x-6\right) = 15x^3-90x^2-14x^2+84x-16x+96 $$ |
| ④ | Combine like terms: $$ 15x^3 \color{blue}{-90x^2} \color{blue}{-14x^2} + \color{red}{84x} \color{red}{-16x} +96 = 15x^3 \color{blue}{-104x^2} + \color{red}{68x} +96 $$ |
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