Question
Answer
$$-4(x-3)^2-(2x+1)=-4x^2+22x-37$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-4(x-3)^2-(2x+1)& \xlongequal{ }-4(x^2-6x+9)-(2x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(4x^2-24x+36)-(2x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-4x^2+24x-36-(2x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-4x^2+24x-36-2x-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-4x^2+22x-37\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4} $ by $ \left( x^2-6x+9\right) $ $$ \color{blue}{4} \cdot \left( x^2-6x+9\right) = 4x^2-24x+36 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(4x^2-24x+36 \right) = -4x^2+24x-36 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2x+1 \right) = -2x-1 $$ |
| ④ | Combine like terms: $$ -4x^2+ \color{blue}{24x} \color{red}{-36} \color{blue}{-2x} \color{red}{-1} = -4x^2+ \color{blue}{22x} \color{red}{-37} $$ |
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