Answer
$$(2x-3)(x-1)(x+5)=2x^3+5x^2-22x+15$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x-3)(x-1)(x+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2-2x-3x+3)(x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2-5x+3)(x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3+10x^2-5x^2-25x+3x+15 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3+5x^2-22x+15\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x-3}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{2x-3}\right) \cdot \left( x-1\right) = 2x^2-2x-3x+3 $$ |
| ② | Combine like terms: $$ 2x^2 \color{blue}{-2x} \color{blue}{-3x} +3 = 2x^2 \color{blue}{-5x} +3 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2-5x+3}\right) $ by each term in $ \left( x+5\right) $. $$ \left( \color{blue}{2x^2-5x+3}\right) \cdot \left( x+5\right) = 2x^3+10x^2-5x^2-25x+3x+15 $$ |
| ④ | Combine like terms: $$ 2x^3+ \color{blue}{10x^2} \color{blue}{-5x^2} \color{red}{-25x} + \color{red}{3x} +15 = 2x^3+ \color{blue}{5x^2} \color{red}{-22x} +15 $$ |
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