Question
Answer
$$(2x-1)(3x-2)(x-1)=6x^3-13x^2+9x-2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x-1)(3x-2)(x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(6x^2-4x-3x+2)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(6x^2-7x+2)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6x^3-6x^2-7x^2+7x+2x-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6x^3-13x^2+9x-2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x-1}\right) $ by each term in $ \left( 3x-2\right) $. $$ \left( \color{blue}{2x-1}\right) \cdot \left( 3x-2\right) = 6x^2-4x-3x+2 $$ |
| ② | Combine like terms: $$ 6x^2 \color{blue}{-4x} \color{blue}{-3x} +2 = 6x^2 \color{blue}{-7x} +2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{6x^2-7x+2}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{6x^2-7x+2}\right) \cdot \left( x-1\right) = 6x^3-6x^2-7x^2+7x+2x-2 $$ |
| ④ | Combine like terms: $$ 6x^3 \color{blue}{-6x^2} \color{blue}{-7x^2} + \color{red}{7x} + \color{red}{2x} -2 = 6x^3 \color{blue}{-13x^2} + \color{red}{9x} -2 $$ |
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