Question
Answer
$$(x-6)(2x-3)(x+4)=2x^3-7x^2-42x+72$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-6)(2x-3)(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2-3x-12x+18)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2-15x+18)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3+8x^2-15x^2-60x+18x+72 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3-7x^2-42x+72\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-6}\right) $ by each term in $ \left( 2x-3\right) $. $$ \left( \color{blue}{x-6}\right) \cdot \left( 2x-3\right) = 2x^2-3x-12x+18 $$ |
| ② | Combine like terms: $$ 2x^2 \color{blue}{-3x} \color{blue}{-12x} +18 = 2x^2 \color{blue}{-15x} +18 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2-15x+18}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{2x^2-15x+18}\right) \cdot \left( x+4\right) = 2x^3+8x^2-15x^2-60x+18x+72 $$ |
| ④ | Combine like terms: $$ 2x^3+ \color{blue}{8x^2} \color{blue}{-15x^2} \color{red}{-60x} + \color{red}{18x} +72 = 2x^3 \color{blue}{-7x^2} \color{red}{-42x} +72 $$ |
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