Question
Answer
$$x(x-9)(x-9)=x^3-18x^2+81x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x(x-9)(x-9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-9x)(x-9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3-9x^2-9x^2+81x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-18x^2+81x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{x} $ by $ \left( x-9\right) $ $$ \color{blue}{x} \cdot \left( x-9\right) = x^2-9x $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2-9x}\right) $ by each term in $ \left( x-9\right) $. $$ \left( \color{blue}{x^2-9x}\right) \cdot \left( x-9\right) = x^3-9x^2-9x^2+81x $$ |
| ③ | Combine like terms: $$ x^3 \color{blue}{-9x^2} \color{blue}{-9x^2} +81x = x^3 \color{blue}{-18x^2} +81x $$ |
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