Question
Answer
$$-3(x+2)^2-5=-3x^2-12x-17$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-3(x+2)^2-5& \xlongequal{ }-3(x^2+4x+4)-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(3x^2+12x+12)-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-3x^2-12x-12-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-3x^2-12x-17\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( x^2+4x+4\right) $ $$ \color{blue}{3} \cdot \left( x^2+4x+4\right) = 3x^2+12x+12 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(3x^2+12x+12 \right) = -3x^2-12x-12 $$ |
| ③ | Combine like terms: $$ -3x^2-12x \color{blue}{-12} \color{blue}{-5} = -3x^2-12x \color{blue}{-17} $$ |
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