Question
Answer
$$-1.7(x-1)(x-12)+30=-x^2+13x+18$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-1.7(x-1)(x-12)+30& \xlongequal{ }-(x-1)(x-12)+30 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(x^2-12x-x+12)+30 \xlongequal{ } \\[1 em] & \xlongequal{ }-(x^2-13x+12)+30 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-x^2+13x-12+30 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-x^2+13x+18\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( x-12\right) $. $$ \left( \color{blue}{x-1}\right) \cdot \left( x-12\right) = x^2-12x-x+12 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(x^2-13x+12 \right) = -x^2+13x-12 $$ |
| ③ | Combine like terms: $$ -x^2+13x \color{blue}{-12} + \color{blue}{30} = -x^2+13x+ \color{blue}{18} $$ |
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