Question
Answer
$$9(x^2-x+1)-x(x-1)=8x^2-8x+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}9(x^2-x+1)-x(x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9x^2-9x+9-(x^2-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9x^2-9x+9-x^2+x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8x^2-8x+9\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{9} $ by $ \left( x^2-x+1\right) $ $$ \color{blue}{9} \cdot \left( x^2-x+1\right) = 9x^2-9x+9 $$Multiply $ \color{blue}{x} $ by $ \left( x-1\right) $ $$ \color{blue}{x} \cdot \left( x-1\right) = x^2-x $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^2-x \right) = -x^2+x $$ |
| ③ | Combine like terms: $$ \color{blue}{9x^2} \color{red}{-9x} +9 \color{blue}{-x^2} + \color{red}{x} = \color{blue}{8x^2} \color{red}{-8x} +9 $$ |
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