Answer
$$(2x^2+5x+15)(-x+5)x=-2x^4+5x^3+10x^2+75x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x^2+5x+15)(-x+5)x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-2x^3+10x^2-5x^2+25x-15x+75)x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(-2x^3+5x^2+10x+75)x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2x^4+5x^3+10x^2+75x\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x^2+5x+15}\right) $ by each term in $ \left( -x+5\right) $. $$ \left( \color{blue}{2x^2+5x+15}\right) \cdot \left( -x+5\right) = -2x^3+10x^2-5x^2+25x-15x+75 $$ |
| ② | Combine like terms: $$ -2x^3+ \color{blue}{10x^2} \color{blue}{-5x^2} + \color{red}{25x} \color{red}{-15x} +75 = -2x^3+ \color{blue}{5x^2} + \color{red}{10x} +75 $$ |
| ③ | $$ \left( \color{blue}{-2x^3+5x^2+10x+75}\right) \cdot x = -2x^4+5x^3+10x^2+75x $$ |
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