Question
Answer
$$(2-x)(x^2-5x+6)+0+x-3=-x^3+7x^2-15x+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2-x)(x^2-5x+6)+0+x-3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2x^2-10x+12-x^3+5x^2-6x+0+x-3 \xlongequal{ } \\[1 em] & \xlongequal{ }2x^2-10x+12-x^3+5x^2-6x0+x-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-x^3+7x^2-15x+9\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2-x}\right) $ by each term in $ \left( x^2-5x+6\right) $. $$ \left( \color{blue}{2-x}\right) \cdot \left( x^2-5x+6\right) = 2x^2-10x+12-x^3+5x^2-6x $$ |
| ② | Combine like terms: $$ \color{blue}{2x^2} \color{red}{-10x} + \color{green}{12} -x^3+ \color{blue}{5x^2} \color{orange}{-6x} \color{blue}{0} + \color{orange}{x} \color{blue}{-3} = -x^3+ \color{blue}{7x^2} \color{orange}{-15x} + \color{blue}{9} $$ |
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