Question
Answer
$$(5x-9)(4x+3)(x-3)=20x^3-81x^2+36x+81$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x-9)(4x+3)(x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(20x^2+15x-36x-27)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(20x^2-21x-27)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}20x^3-60x^2-21x^2+63x-27x+81 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}20x^3-81x^2+36x+81\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5x-9}\right) $ by each term in $ \left( 4x+3\right) $. $$ \left( \color{blue}{5x-9}\right) \cdot \left( 4x+3\right) = 20x^2+15x-36x-27 $$ |
| ② | Combine like terms: $$ 20x^2+ \color{blue}{15x} \color{blue}{-36x} -27 = 20x^2 \color{blue}{-21x} -27 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{20x^2-21x-27}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{20x^2-21x-27}\right) \cdot \left( x-3\right) = 20x^3-60x^2-21x^2+63x-27x+81 $$ |
| ④ | Combine like terms: $$ 20x^3 \color{blue}{-60x^2} \color{blue}{-21x^2} + \color{red}{63x} \color{red}{-27x} +81 = 20x^3 \color{blue}{-81x^2} + \color{red}{36x} +81 $$ |
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