Answer
$$(7x-9)(2x+1)(x-5)=14x^3-81x^2+46x+45$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7x-9)(2x+1)(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(14x^2+7x-18x-9)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(14x^2-11x-9)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}14x^3-70x^2-11x^2+55x-9x+45 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}14x^3-81x^2+46x+45\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{7x-9}\right) $ by each term in $ \left( 2x+1\right) $. $$ \left( \color{blue}{7x-9}\right) \cdot \left( 2x+1\right) = 14x^2+7x-18x-9 $$ |
| ② | Combine like terms: $$ 14x^2+ \color{blue}{7x} \color{blue}{-18x} -9 = 14x^2 \color{blue}{-11x} -9 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{14x^2-11x-9}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{14x^2-11x-9}\right) \cdot \left( x-5\right) = 14x^3-70x^2-11x^2+55x-9x+45 $$ |
| ④ | Combine like terms: $$ 14x^3 \color{blue}{-70x^2} \color{blue}{-11x^2} + \color{red}{55x} \color{red}{-9x} +45 = 14x^3 \color{blue}{-81x^2} + \color{red}{46x} +45 $$ |
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