Question
Answer
$$x^{16}(x+2)(x-3)(2x-1)=2x^{19}-3x^{18}-11x^{17}+6x^{16}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x^{16}(x+2)(x-3)(2x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^{17}+2x^{16})(x-3)(2x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^{18}-3x^{17}+2x^{17}-6x^{16})(2x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^{18}-x^{17}-6x^{16})(2x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^{19}-x^{18}-2x^{18}+x^{17}-12x^{17}+6x^{16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2x^{19}-3x^{18}-11x^{17}+6x^{16}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{x^{16}} $ by $ \left( x+2\right) $ $$ \color{blue}{x^{16}} \cdot \left( x+2\right) = x^{17}+2x^{16} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^{17}+2x^{16}}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{x^{17}+2x^{16}}\right) \cdot \left( x-3\right) = x^{18}-3x^{17}+2x^{17}-6x^{16} $$ |
| ③ | Combine like terms: $$ x^{18} \color{blue}{-3x^{17}} + \color{blue}{2x^{17}} -6x^{16} = x^{18} \color{blue}{-x^{17}} -6x^{16} $$ |
| ④ | Multiply each term of $ \left( \color{blue}{x^{18}-x^{17}-6x^{16}}\right) $ by each term in $ \left( 2x-1\right) $. $$ \left( \color{blue}{x^{18}-x^{17}-6x^{16}}\right) \cdot \left( 2x-1\right) = 2x^{19}-x^{18}-2x^{18}+x^{17}-12x^{17}+6x^{16} $$ |
| ⑤ | Combine like terms: $$ 2x^{19} \color{blue}{-x^{18}} \color{blue}{-2x^{18}} + \color{red}{x^{17}} \color{red}{-12x^{17}} +6x^{16} = 2x^{19} \color{blue}{-3x^{18}} \color{red}{-11x^{17}} +6x^{16} $$ |
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