Answer
$$(2x-9)(x-4)(2x+9)=4x^3-16x^2-81x+324$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x-9)(x-4)(2x+9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2-8x-9x+36)(2x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2-17x+36)(2x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^3+18x^2-34x^2-153x+72x+324 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4x^3-16x^2-81x+324\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x-9}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{2x-9}\right) \cdot \left( x-4\right) = 2x^2-8x-9x+36 $$ |
| ② | Combine like terms: $$ 2x^2 \color{blue}{-8x} \color{blue}{-9x} +36 = 2x^2 \color{blue}{-17x} +36 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2-17x+36}\right) $ by each term in $ \left( 2x+9\right) $. $$ \left( \color{blue}{2x^2-17x+36}\right) \cdot \left( 2x+9\right) = 4x^3+18x^2-34x^2-153x+72x+324 $$ |
| ④ | Combine like terms: $$ 4x^3+ \color{blue}{18x^2} \color{blue}{-34x^2} \color{red}{-153x} + \color{red}{72x} +324 = 4x^3 \color{blue}{-16x^2} \color{red}{-81x} +324 $$ |
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