Answer
$$(x-8)(x+1)(7x-5)=7x^3-54x^2-21x+40$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-8)(x+1)(7x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+x-8x-8)(7x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-7x-8)(7x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}7x^3-5x^2-49x^2+35x-56x+40 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}7x^3-54x^2-21x+40\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-8}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x-8}\right) \cdot \left( x+1\right) = x^2+x-8x-8 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{x} \color{blue}{-8x} -8 = x^2 \color{blue}{-7x} -8 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-7x-8}\right) $ by each term in $ \left( 7x-5\right) $. $$ \left( \color{blue}{x^2-7x-8}\right) \cdot \left( 7x-5\right) = 7x^3-5x^2-49x^2+35x-56x+40 $$ |
| ④ | Combine like terms: $$ 7x^3 \color{blue}{-5x^2} \color{blue}{-49x^2} + \color{red}{35x} \color{red}{-56x} +40 = 7x^3 \color{blue}{-54x^2} \color{red}{-21x} +40 $$ |
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