Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+7.5)(x+4)(x-1)(x-10)(x-11)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+4x+7x+28)(x-1)(x-10)(x-11) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+11x+28)(x-1)(x-10)(x-11) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3-x^2+11x^2-11x+28x-28)(x-10)(x-11) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3+10x^2+17x-28)(x-10)(x-11) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}(x^4-83x^2-198x+280)(x-11) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}x^5-11x^4-83x^3+715x^2+2458x-3080\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+7}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{x+7}\right) \cdot \left( x+4\right) = x^2+4x+7x+28 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{4x} + \color{blue}{7x} +28 = x^2+ \color{blue}{11x} +28 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+11x+28}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{x^2+11x+28}\right) \cdot \left( x-1\right) = x^3-x^2+11x^2-11x+28x-28 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-x^2} + \color{blue}{11x^2} \color{red}{-11x} + \color{red}{28x} -28 = x^3+ \color{blue}{10x^2} + \color{red}{17x} -28 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3+10x^2+17x-28}\right) $ by each term in $ \left( x-10\right) $. $$ \left( \color{blue}{x^3+10x^2+17x-28}\right) \cdot \left( x-10\right) = \\ = x^4 -\cancel{10x^3}+ \cancel{10x^3}-100x^2+17x^2-170x-28x+280 $$ |
| ⑥ | Combine like terms: $$ x^4 \, \color{blue}{ -\cancel{10x^3}} \,+ \, \color{blue}{ \cancel{10x^3}} \, \color{green}{-100x^2} + \color{green}{17x^2} \color{orange}{-170x} \color{orange}{-28x} +280 = x^4 \color{green}{-83x^2} \color{orange}{-198x} +280 $$ |
| ⑦ | Multiply each term of $ \left( \color{blue}{x^4-83x^2-198x+280}\right) $ by each term in $ \left( x-11\right) $. $$ \left( \color{blue}{x^4-83x^2-198x+280}\right) \cdot \left( x-11\right) = x^5-11x^4-83x^3+913x^2-198x^2+2178x+280x-3080 $$ |
| ⑧ | Combine like terms: $$ x^5-11x^4-83x^3+ \color{blue}{913x^2} \color{blue}{-198x^2} + \color{red}{2178x} + \color{red}{280x} -3080 = x^5-11x^4-83x^3+ \color{blue}{715x^2} + \color{red}{2458x} -3080 $$ |