Question
Answer
$$x^2+6x-(3x-6)^2=-8x^2+42x-36$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x^2+6x-(3x-6)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2+6x-(9x^2-36x+36) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2+6x-9x^2+36x-36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-8x^2+42x-36\end{aligned} $$ | |
| ① | Find $ \left(3x-6\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3x } $ and $ B = \color{red}{ 6 }$. $$ \begin{aligned}\left(3x-6\right)^2 = \color{blue}{\left( 3x \right)^2} -2 \cdot 3x \cdot 6 + \color{red}{6^2} = 9x^2-36x+36\end{aligned} $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 9x^2-36x+36 \right) = -9x^2+36x-36 $$ |
| ③ | Combine like terms: $$ \color{blue}{x^2} + \color{red}{6x} \color{blue}{-9x^2} + \color{red}{36x} -36 = \color{blue}{-8x^2} + \color{red}{42x} -36 $$ |
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