Answer
$$(2x-1)(x-5)(x+6)=2x^3+x^2-61x+30$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x-1)(x-5)(x+6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2-10x-x+5)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2-11x+5)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3+12x^2-11x^2-66x+5x+30 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3+x^2-61x+30\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x-1}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{2x-1}\right) \cdot \left( x-5\right) = 2x^2-10x-x+5 $$ |
| ② | Combine like terms: $$ 2x^2 \color{blue}{-10x} \color{blue}{-x} +5 = 2x^2 \color{blue}{-11x} +5 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2-11x+5}\right) $ by each term in $ \left( x+6\right) $. $$ \left( \color{blue}{2x^2-11x+5}\right) \cdot \left( x+6\right) = 2x^3+12x^2-11x^2-66x+5x+30 $$ |
| ④ | Combine like terms: $$ 2x^3+ \color{blue}{12x^2} \color{blue}{-11x^2} \color{red}{-66x} + \color{red}{5x} +30 = 2x^3+ \color{blue}{x^2} \color{red}{-61x} +30 $$ |
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