Question
Answer
$$(6x-9)(3x+2)(x-3)=18x^3-69x^2+27x+54$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(6x-9)(3x+2)(x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(18x^2+12x-27x-18)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(18x^2-15x-18)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}18x^3-54x^2-15x^2+45x-18x+54 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}18x^3-69x^2+27x+54\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{6x-9}\right) $ by each term in $ \left( 3x+2\right) $. $$ \left( \color{blue}{6x-9}\right) \cdot \left( 3x+2\right) = 18x^2+12x-27x-18 $$ |
| ② | Combine like terms: $$ 18x^2+ \color{blue}{12x} \color{blue}{-27x} -18 = 18x^2 \color{blue}{-15x} -18 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{18x^2-15x-18}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{18x^2-15x-18}\right) \cdot \left( x-3\right) = 18x^3-54x^2-15x^2+45x-18x+54 $$ |
| ④ | Combine like terms: $$ 18x^3 \color{blue}{-54x^2} \color{blue}{-15x^2} + \color{red}{45x} \color{red}{-18x} +54 = 18x^3 \color{blue}{-69x^2} + \color{red}{27x} +54 $$ |
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