Question
Answer
$$(6x-9)(3x+3)(x-5)=18x^3-99x^2+18x+135$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(6x-9)(3x+3)(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(18x^2+18x-27x-27)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(18x^2-9x-27)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}18x^3-90x^2-9x^2+45x-27x+135 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}18x^3-99x^2+18x+135\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{6x-9}\right) $ by each term in $ \left( 3x+3\right) $. $$ \left( \color{blue}{6x-9}\right) \cdot \left( 3x+3\right) = 18x^2+18x-27x-27 $$ |
| ② | Combine like terms: $$ 18x^2+ \color{blue}{18x} \color{blue}{-27x} -27 = 18x^2 \color{blue}{-9x} -27 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{18x^2-9x-27}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{18x^2-9x-27}\right) \cdot \left( x-5\right) = 18x^3-90x^2-9x^2+45x-27x+135 $$ |
| ④ | Combine like terms: $$ 18x^3 \color{blue}{-90x^2} \color{blue}{-9x^2} + \color{red}{45x} \color{red}{-27x} +135 = 18x^3 \color{blue}{-99x^2} + \color{red}{18x} +135 $$ |
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