Answer
$$(2x-3)(x-1)(x-3)=2x^3-11x^2+18x-9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x-3)(x-1)(x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2-2x-3x+3)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2-5x+3)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3-6x^2-5x^2+15x+3x-9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3-11x^2+18x-9\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x-3}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{2x-3}\right) \cdot \left( x-1\right) = 2x^2-2x-3x+3 $$ |
| ② | Combine like terms: $$ 2x^2 \color{blue}{-2x} \color{blue}{-3x} +3 = 2x^2 \color{blue}{-5x} +3 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2-5x+3}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{2x^2-5x+3}\right) \cdot \left( x-3\right) = 2x^3-6x^2-5x^2+15x+3x-9 $$ |
| ④ | Combine like terms: $$ 2x^3 \color{blue}{-6x^2} \color{blue}{-5x^2} + \color{red}{15x} + \color{red}{3x} -9 = 2x^3 \color{blue}{-11x^2} + \color{red}{18x} -9 $$ |
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