Answer
$$(5x-9)(2x+2)(x-4)=10x^3-48x^2+14x+72$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x-9)(2x+2)(x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(10x^2+10x-18x-18)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(10x^2-8x-18)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}10x^3-40x^2-8x^2+32x-18x+72 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}10x^3-48x^2+14x+72\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5x-9}\right) $ by each term in $ \left( 2x+2\right) $. $$ \left( \color{blue}{5x-9}\right) \cdot \left( 2x+2\right) = 10x^2+10x-18x-18 $$ |
| ② | Combine like terms: $$ 10x^2+ \color{blue}{10x} \color{blue}{-18x} -18 = 10x^2 \color{blue}{-8x} -18 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{10x^2-8x-18}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{10x^2-8x-18}\right) \cdot \left( x-4\right) = 10x^3-40x^2-8x^2+32x-18x+72 $$ |
| ④ | Combine like terms: $$ 10x^3 \color{blue}{-40x^2} \color{blue}{-8x^2} + \color{red}{32x} \color{red}{-18x} +72 = 10x^3 \color{blue}{-48x^2} + \color{red}{14x} +72 $$ |
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