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