Answer
$$(5x-8)(2x+3)(x-5)=10x^3-51x^2-19x+120$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x-8)(2x+3)(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(10x^2+15x-16x-24)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(10x^2-x-24)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}10x^3-50x^2-x^2+5x-24x+120 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}10x^3-51x^2-19x+120\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5x-8}\right) $ by each term in $ \left( 2x+3\right) $. $$ \left( \color{blue}{5x-8}\right) \cdot \left( 2x+3\right) = 10x^2+15x-16x-24 $$ |
| ② | Combine like terms: $$ 10x^2+ \color{blue}{15x} \color{blue}{-16x} -24 = 10x^2 \color{blue}{-x} -24 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{10x^2-x-24}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{10x^2-x-24}\right) \cdot \left( x-5\right) = 10x^3-50x^2-x^2+5x-24x+120 $$ |
| ④ | Combine like terms: $$ 10x^3 \color{blue}{-50x^2} \color{blue}{-x^2} + \color{red}{5x} \color{red}{-24x} +120 = 10x^3 \color{blue}{-51x^2} \color{red}{-19x} +120 $$ |
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