Question
Answer
$$6x(x-3)(x-2)=6x^3-30x^2+36x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6x(x-3)(x-2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(6x^2-18x)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6x^3-12x^2-18x^2+36x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6x^3-30x^2+36x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{6x} $ by $ \left( x-3\right) $ $$ \color{blue}{6x} \cdot \left( x-3\right) = 6x^2-18x $$ |
| ② | Multiply each term of $ \left( \color{blue}{6x^2-18x}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{6x^2-18x}\right) \cdot \left( x-2\right) = 6x^3-12x^2-18x^2+36x $$ |
| ③ | Combine like terms: $$ 6x^3 \color{blue}{-12x^2} \color{blue}{-18x^2} +36x = 6x^3 \color{blue}{-30x^2} +36x $$ |
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