Question
Answer
$$(x+6)(x-1)(2x+7)=2x^3+17x^2+23x-42$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+6)(x-1)(2x+7)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-x+6x-6)(2x+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+5x-6)(2x+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3+7x^2+10x^2+35x-12x-42 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3+17x^2+23x-42\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+6}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{x+6}\right) \cdot \left( x-1\right) = x^2-x+6x-6 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-x} + \color{blue}{6x} -6 = x^2+ \color{blue}{5x} -6 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+5x-6}\right) $ by each term in $ \left( 2x+7\right) $. $$ \left( \color{blue}{x^2+5x-6}\right) \cdot \left( 2x+7\right) = 2x^3+7x^2+10x^2+35x-12x-42 $$ |
| ④ | Combine like terms: $$ 2x^3+ \color{blue}{7x^2} + \color{blue}{10x^2} + \color{red}{35x} \color{red}{-12x} -42 = 2x^3+ \color{blue}{17x^2} + \color{red}{23x} -42 $$ |
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