Question
Answer
$$-3(2x-3)^2+4(x+2)^2=-8x^2+52x-11$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-3(2x-3)^2+4(x+2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-3(4x^2-12x+9)+4(x^2+4x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(12x^2-36x+27)+4x^2+16x+16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-12x^2+36x-27+4x^2+16x+16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-8x^2+52x-11\end{aligned} $$ | |
| ① | Find $ \left(x+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(x+2\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 2 + \color{red}{2^2} = x^2+4x+4\end{aligned} $$ |
| ② | Multiply $ \color{blue}{3} $ by $ \left( 4x^2-12x+9\right) $ $$ \color{blue}{3} \cdot \left( 4x^2-12x+9\right) = 12x^2-36x+27 $$Multiply $ \color{blue}{4} $ by $ \left( x^2+4x+4\right) $ $$ \color{blue}{4} \cdot \left( x^2+4x+4\right) = 4x^2+16x+16 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(12x^2-36x+27 \right) = -12x^2+36x-27 $$ |
| ④ | Combine like terms: $$ \color{blue}{-12x^2} + \color{red}{36x} \color{green}{-27} + \color{blue}{4x^2} + \color{red}{16x} + \color{green}{16} = \color{blue}{-8x^2} + \color{red}{52x} \color{green}{-11} $$ |
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