Question
Answer
$$-3(2x+5)^2+10=-12x^2-60x-65$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-3(2x+5)^2+10& \xlongequal{ }-3(4x^2+20x+25)+10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(12x^2+60x+75)+10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-12x^2-60x-75+10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-12x^2-60x-65\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( 4x^2+20x+25\right) $ $$ \color{blue}{3} \cdot \left( 4x^2+20x+25\right) = 12x^2+60x+75 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(12x^2+60x+75 \right) = -12x^2-60x-75 $$ |
| ③ | Combine like terms: $$ -12x^2-60x \color{blue}{-75} + \color{blue}{10} = -12x^2-60x \color{blue}{-65} $$ |
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