Question
Answer
$$(6x-8)(2x+3)(x-4)=12x^3-46x^2-32x+96$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(6x-8)(2x+3)(x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(12x^2+18x-16x-24)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(12x^2+2x-24)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}12x^3-48x^2+2x^2-8x-24x+96 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}12x^3-46x^2-32x+96\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{6x-8}\right) $ by each term in $ \left( 2x+3\right) $. $$ \left( \color{blue}{6x-8}\right) \cdot \left( 2x+3\right) = 12x^2+18x-16x-24 $$ |
| ② | Combine like terms: $$ 12x^2+ \color{blue}{18x} \color{blue}{-16x} -24 = 12x^2+ \color{blue}{2x} -24 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{12x^2+2x-24}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{12x^2+2x-24}\right) \cdot \left( x-4\right) = 12x^3-48x^2+2x^2-8x-24x+96 $$ |
| ④ | Combine like terms: $$ 12x^3 \color{blue}{-48x^2} + \color{blue}{2x^2} \color{red}{-8x} \color{red}{-24x} +96 = 12x^3 \color{blue}{-46x^2} \color{red}{-32x} +96 $$ |
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