Question
Answer
$$-4(x-1)^2+8=-4x^2+8x+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-4(x-1)^2+8& \xlongequal{ }-4(x^2-2x+1)+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(4x^2-8x+4)+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-4x^2+8x-4+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-4x^2+8x+4\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4} $ by $ \left( x^2-2x+1\right) $ $$ \color{blue}{4} \cdot \left( x^2-2x+1\right) = 4x^2-8x+4 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(4x^2-8x+4 \right) = -4x^2+8x-4 $$ |
| ③ | Combine like terms: $$ -4x^2+8x \color{blue}{-4} + \color{blue}{8} = -4x^2+8x+ \color{blue}{4} $$ |
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