Question
Answer
$$-4(x-2)^2+4=-4x^2+16x-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-4(x-2)^2+4& \xlongequal{ }-4(x^2-4x+4)+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(4x^2-16x+16)+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-4x^2+16x-16+4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-4x^2+16x-12\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4} $ by $ \left( x^2-4x+4\right) $ $$ \color{blue}{4} \cdot \left( x^2-4x+4\right) = 4x^2-16x+16 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(4x^2-16x+16 \right) = -4x^2+16x-16 $$ |
| ③ | Combine like terms: $$ -4x^2+16x \color{blue}{-16} + \color{blue}{4} = -4x^2+16x \color{blue}{-12} $$ |
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